@STRING{cahiers = "Cah\-iers de Topo\-lo\-gie et G\'e\-o\-m\'e\-trie Dif\-f\'e\-ren\-ti\-elle Cat\-\'e\-go\-rique" } @STRING{oldcahiers = "Cah\-iers de Topo\-lo\-gie et G\'e\-o\-m\'e\-trie Dif\-f\'e\-ren\-ti\-elle" } @STRING{ams = "Ameri\-can Mathe\-mati\-cal Society"} @STRING{lnm = "Lec\-ture Notes in Math\-e\-ma\-tics"} @STRING{lncs = "Lec\-ture Notes in Com\-pu\-ter Sci\-ence"} @STRING{jpaa = "Journal of Pure and Applied Algebra"} @STRING{springer = "Sprin\-ger-Ver\-lag"} @STRING{diagrammes = "Dia\-gram\-mes"} @STRING{esquisses = "Esquis\-ses Math\'e\-ma\-tiques"} @STRING{MSCS = "Mathematical Structures in Computer Science"} @ARTICLE{a&ros, author="Ad\'amek, Ji\v{r}\'i and Ji\v{r}\'i Rosi\v{c}ky", title = "On injectivity in locally presentable categories", journal = "Transactions of the American Mathematical Society", volume = 336, number=2, year = 1991, } @BOOK{arbook, author="Ad\'amek, Ji\v{r}\'i and Ji\v{r}\'i Rosi\v{c}ky", title = "Locally Presentable and Accessible Categories", publisher = "Cambridge University Press", year = 1994, note = "(Note: The title may have been changed. The ISBN number is 0-521-42261-2.)", } @ARTICLE{ageron89, author = "Ag\'e\-ron, Pierre", title = "S\'eman\-ti\-que cat\'ego\-ri\-que des constructeurs de types d'ordre sup\'e\-ri\-eur", journal = diagrammes, year = "1989", volume = "22", pages = "31--44", } @PHDTHESIS{agthesis, author = "Ag\'e\-ron, Pierre", title = "Structure des Logiques et Logique des Structures: Logiques, Cat\'e\-gories, Esquis\-ses", school = "Univer\-sit\'e Paris 7", year = "1991", } @ARTICLE{ageron92, author = "Ag\'e\-ron, Pierre", title = "The logic of structures", journal = jpaa, year = "1992", volume = "79", pages = "15--34", } @ARTICLE{and&nem, author = "Andr\'eka, H. and I. N\'emeti", title = "Formulas and ultraproducts in categories", journal = "Beit. zur Alg. und Geom.", volume = 8, year = 1979 } @ARTICLE{and&neminj, author = "Andr\'eka, H. and I. N\'emeti", title = "Injectivity in categories to represent all first order formulas {I}", journal = "Dem. Math.", volume = "XII", number = 3, year = 1979 } @ARTICLE{barrmodsketch, author = "Barr, Michael", title = "Models of Sketches", journal = cahiers, year = "1986", volume = "27", pages = "93--107", } @ARTICLE{barrhornth, author = "Barr, Michael", title = "Models of {H}orn Theories", journal = "Contemporary Mathematics", year = "1989", volume = "92", pages = "1--7", } @BOOK{ttt, author = "Barr, Michael and Charles Wells", title = "Toposes, Triples and Theories", publisher = springer, year = "1985", series = "Grundlehren der mathematischen Wissenschaften", volume = "278", address = "New York", note = "A list of corrections and additions is maintained in \cite{tttcorr}.", } @BOOKLET{tttcorr, author = "Barr, Michael and Charles Wells", title = "Corrections to {T}oposes, {T}riples and {T}heories", year = "1993", note = "Corrections and additions to \cite{ttt}.", howpublished = "Available by anonymous FTP from {\tt triples.math.mcgill.ca} in directory {\tt pub/barr}", } @BOOK{ctcs, author = "Barr, Michael and Charles Wells", title = "Category Theory for Computing Science", publisher = "Prentice-Hall International", year = "1990", series = "Prentice-Hall International Series in Computer Science", address = "New York", note = "The document \cite{ctcsup} contains corrections and additions to the book.", } @BOOKLET{ctcsup, author = "Barr, Michael and Charles Wells", title = "Category {T}heory for {C}omputing {S}cience: Update", year = "1993", note = "Corrections and additions to \cite{ctcs}.", howpublished = "Available by anonymous FTP from {\tt triples.math.mcgill.ca} in directory {\tt pub/barr}. The file is called {\tt ctcsupdate.dvi}", } @ARTICLE{limsk, author = "Barr, Michael and Charles Wells", title = "On the limitations of sketches", journal = "Canadian Mathematical Bulletin", year = "1992", volume = "35", pages = "287--294", } @BOOKLET{diagc, author = "Barr, Michael and Charles Wells", title = "The Category of Diagrams", year = "1993", note = "To appear in the Journal of Pure and Applied Algebra", } @ARTICLE{bastcomp, author = "Bastiani, Andr\'ee", title = "Sketched Structures and Completions", journal =oldcahiers, year = "1973", volume = "14", pages = "158-160", } @ARTICLE{bastehres, author = "Bastiani, Andr\'ee and Charles Ehresmann", title = "Categories of Sketched Structures", journal = oldcahiers, year = "1972", volume = "13", pages = "104-213", } @BOOK{bell88, author = "Bell, J.L.", title = "Toposes and Local Set Theories: An Introduction", publisher = "Oxford University Press", year = "1988", series = "Oxford Logic Guides", } @ARTICLE{benaboustruc, author = "B\'enabou, Jean", title = "Structures algebriques dans les categories", journal = oldcahiers, year = "1972", volume = "13", pages = "103-214", } @ARTICLE{bkpm, author = "Blackwell, R. and G.M. Kelly and A.J. Power", title = "Two-Dimensional Monad Theory", journal = "The Journal of Pure and Applied Algebra", year = "1989", volume = "59", pages = "1--41", } @ARTICLE{boileaujoyal, author = "Boileau, A. and A. Joyal", title = "La Logique des Topos", journal = "Symbolic Logic", year = "1981", volume = "46", pages = "6--16", } @BOOKLET{borvit, author = "Borceux, Francis and Enrico Vitale", title = "A {M}orita Theorem for Algebraic Theories", year = "1991", note = "Preprint", } @ARTICLE{bunge84, author = "Bunge, Marta C.", title = "Toposes in Logic and Logic in Toposes", journal = "Topoi", year = "1984", volume = "3", pages = "13--22", } @ARTICLE{burr, author = "Burroni, Albert", title = "Esquis\-ses des cat\'e\-gories \`a limites et des quasi-topologies", journal = esquisses, year = "1970", volume = "5", } @ARTICLE{burr70, author = "Burroni, E.", title = "Cat\'e\-go\-ries Dis\-crete\-ment Struc\-tur\'ees", journal = esquisses, year = "1970", volume = "5", } @ARTICLE{burr81, author = "Burroni, A.", title = "Alg\'ebres graphi\-ques", journal = oldcahiers, year = "1981", volume = "XXII", } @ARTICLE{cartmell86, author = "Cartmell, J.", title = "Generalized Algebraic Theories and Contextual Categories", journal = "Annals Pure Applied Logic", year = "1986", volume = "32", pages = "209--243", note = "A different approach to models of finite limit theories.", } @ARTICLE{ladc, author = "Cockett, J. Robin", title = "List-arithmetic Distributive Categories: Locoi", journal = jpaa, year = "1990", volume = "66", pages = "1-29", } @BOOKLET{conduche, author = "Conduche, F.", title = "Definition des Topos Elementaires par Limi\-tes Projec\-tives Finies", year = "1973", address = "Paris", howpublished = "Notes", } @ARTICLE{copp72, author = "Coppey, L.", title = "Th\'eo\-ries Alg\'ebri\-ques et Extensions de Pr\'efaisceaux, et Compl\'e\-ments", journal = oldcahiers, year = "1972", volume = "XIII", number = "1 et 3", } @ARTICLE{coppeygraph, author = "Coppey, L.", title = "Graphes Structuraux", journal = diagrammes, year = "1990", volume = "24", pages = "33--75", } @ARTICLE{coppeylair84, author = "Coppey, L. and C. Lair", title = "Le\c cons de Th\'eorie des Esquis\-ses", journal = diagrammes, year = "1984", volume = "12", } @ARTICLE{coppeylair85, author = "Coppey, L. and C. Lair", title = "Alg\'ebricit\'e, Mona\-dicit\'e, Esquis\-sa\-bi\-lit\'e et Non-alg\'ebricit\'e", journal = diagrammes, year = "1985", volume = "13", } @ARTICLE{coppeylair88, author = "Coppey, L. and C. Lair", title = "Le\c cons de Th\'eorie des Esquis\-ses, Partie~{II}", journal = diagrammes, year = "1988", volume = "19", note = "Contains many elementary examples of sketches.", } @INCOLLECTION{costele, author = "Coste, Michel", title = "Une approche logi\-que des th\'eories d\'efi\-nis\-sa\-bles par limi\-tes pro\-jec\-ti\-ves finies", booktitle = "S\'emi\-naire B\'ena\-bou", year = "1976", publisher = "Uni\-ver\-sit\'e Paris-Nord", } @ARTICLE{daystreet, author = "Day, Brian and Ross Street", title = "Localisations of Locally Presentable Categories~{II}", journal = jpaa, year = "1990", volume = "63", pages = "225--229", } @PHDTHESIS{diersthesis, author = "Diers, Y.", title = "Cat\'e\-go\-ries Localizables", school = "Univer\-sit\'e de Paris", year = "1977", } @ARTICLE{duvrey1, author = "Duval, Dominique and Jean-Claude Reynaud", title = "Sketches and computation (1)", journal = MSCS, year = "1994", } @ARTICLE{duvrey2, author = "Duval, Dominique and Jean-Claude Reynaud", title = "Sketches and computation (2)", journal = MSCS, year = "1994", } @ARTICLE{duvsen, author = "Duval, Dominique and Pascale S\'en\'echaud", title = "Sketches and parametrization", journal =TCS, year = "1994", } @INCOLLECTION{dybjer86, author = "Dybjer, P.", title = "Category Theory and Programming Language Semantics: an Overview", pages = "165-181", editor = "Pitt, D.", booktitle = "Category Theory and Computer Programming", series = lncs, volume = "240", year = "1986", publisher = springer, } @TECHREPORT{ehrkan, author = "Ehresmann, Charles", title = "Introduction to the Theory of Structured Categories", institution = "University of Kansas", number = "10", year = "1966", } @ARTICLE{csg, author = "Ehresmann, Charles", title = "Cat\'e\-gories struc\-tur\'ees g\'en\'e\-ralis\'es", journal = oldcahiers, volume = "X", year = "1968", pages = "139--168", } @ARTICLE{ehres68, author = "Ehresmann, Charles", title = "Esquis\-ses et types des struc\-tu\-res alg\'ebri\-ques", journal = "Bul. Inst. Polit. Ia\c si", volume = "XIV", year = "1968", } @INCOLLECTION{ehres69, author = "Ehresmann, Charles", title = "Construction de structures libres", editor = "Hilton, Peter", booktitle = "Category Theory, Homology Theory and their Applications~{II}", series = lnm, volume = "92", year = "1969", publisher = springer, note = "I have not read this", } @BOOK{ehrigmahr, author = "Ehrig, Helmut and B. Mahr", title = "Fundamentals of Algebraic Specifications~{I}", publisher = springer, year ="1985", } @ARTICLE{elkzil, author = "Elkins, B. and J. Zilber", title = "Categories of Actions and {M}orita Equivalences", journal = "Rocky Mountain Mathematical Journal", year = "1976", volume = "6", pages = "199--225", } @BOOKLET{evag, author = "Even, C. and P. Ag\'eron", title = "Ag\'eron, Rapport de Stage de Diplome d'Etudes Approfondies", year = "1987", address = "Paris", } @BOOKLET{fishpalm, author = "Fisher-Palmquist, J. and P. H. Palmquist", title = "{M}orita Contexts and Equivalences of Enriched Functor Categories", year = "1973", } @ARTICLE{foltzlair, title = "Fermeture standard des cat\'e\-go\-ries al'e\-bri\-ques", author = "Foltz, F. and Christian Lair", journal = oldcahiers, year = "1972", volume = "13", pages = "275--307", } @ARTICLE{foltzlairkelly, title = "Algebraic categories with few monoidal biclosed structures or none", author = "Foltz, F. and Christian Lair and G. M. Kelly", journal = jpaa, year = "1980", pages = "171--177", } @INCOLLECTION{fourmanlogic, author = "Fourman, Michael", title = "The Logic of Topoi", editor = "Barwise, J. and others", booktitle = "Handbook of Mathematical Logic", publisher = "North-Holland", year = "1977", } @INCOLLECTION{fourvick, author = "Fourman, Michael and S. Vickers", title = "Theories as categories", booktitle = "Category Theory and Computer Programming", editor = "Pitt, D. and others", series = lncs, volume = "240", publisher = springer, year = "1986", pages = "434--448", } @ARTICLE{freyd66, author = "Freyd, Peter", title = "Algebra valued functors in general and tensor products in particular", journal = "Colloquium Mathematicum", volume = "14", year = "1966", pages = "89--106", } @ARTICLE{auspaper, author = "Freyd, Peter", title = "Aspects of topoi", journal = "Bulletin of the Australian Mathematical Society", volume = "7", year = "1972", pages = "1--72", } @ARTICLE{auscorr, author = "Freyd, Peter", title = "Aspects of topoi: Corrigenda and acknowledgements", journal = "Bulletin of the Australian Mathematical Society", volume = "7", year = "1972", pages = "467--480", } @BOOK{gabrielulmer, author = "Gabriel, Peter and Friedrich Ulmer", title = "Lokal Pr\umlaut a\-sen\-tier\-bare Kate\-go\-rien", series = lnm, year = "1971", volume = "221", publisher = springer, note = "Contains the characterization of categories of models of finite-limit sketches.", } @INCOLLECTION{gogtype, author = "Goguen, Joseph A.", title = "Types as Theories", booktitle = "Proceedings of Symposium on General Topology and Applications", year = "1990", publisher = "Oxford University Press", } @INCOLLECTION{gogburst, author = "Goguen, Joseph A. and R. M. Burstall", title = "A Study in the Foundations of Programming Methodology: Specifications, Institutions, Charters and Parchments", editor = "Pitt, D. and others", booktitle = "Category Theory and Computer Programming", series = lncs, volume = "240", publisher = springer, year = "1986", pages = "313--333", } @ARTICLE{gogmes, author = "Goguen, Joseph A. and Jos\'e Meseguer", title = "Completeness of Many-Sorted Equational Logic", journal = "Houston Journal of Mathematics", volume = 11, number = 3, year = 1985, } @INCOLLECTION{gogthatcherwright, author = "Goguen, Joseph A. and J.W. Thatcher and E.G. Wagner", title = "An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types", editor = "Yeh, R.", booktitle = "Current Trends in Programming Methodology~{IV}", publisher = "Prentice-Hall", year = "1978", pages = "80--149", } @ARTICLE{gray87, author = "Gray, John W.", title = "Categorical Aspects of Data Type Constructors", journal = "Theoretical Computer Science", year = "1987", volume = "50", pages = "103--135", } @INCOLLECTION{gray89, author = "Gray, John W.", title = "The Category of Sketches as a Model for Algebraic Semantics", pages = "109--135", editor = "John W. Gray and Andre Scedrov", booktitle = "Categories in Computer Science and Logic", series = "Contemporary Mathematics", publisher = ams, volume = "92", year = "1989", } @ARTICLE{gray90, author = "Gray, John W.", title = "Executable Specifications for Data-Type Constructors", journal = diagrammes, year = "1990", volume = "24", pages = "7--31", } @ARTICLE{grayreview, author = "Gray, John W.", title = "Review of ``{A}ccessible {C}ategories: {T}he {F}oundations of {C}ategorical {M}odel {T}heory, by {M}ichael {M}akkai and {R}obert {P}ar\'e''", journal = "Bulletin (New Series) of the American Mathematical Society", year = "1991", volume = "25", pages = "131--140", } @INCOLLECTION{graylambda, author = "Gray, John W.", title = "Order-Enriched Sketches for Typed Lambda Calculi", booktitle = "Category Theory", editor = "Carboni, A. and M. C. Pedicchio and G. Rosolini", pages = "105--130", year = 1991, publisher = springer, series = lnm, volume = 1488, } @BOOK{grayscedrov, author = "Gray, John W. and Andre Scedrov", title = "Categories in Computer Science and Logic", series = "Contemporary Mathematics", volume = "92", year = "1989", publisher = ams, } @ARTICLE{guitartgeom, author = "Guitart, Ren\'e", title = "On the Geometry of Computations ({I})", journal = cahiers, year = "1986", volume = "27", pages = "107--136", } @ARTICLE{guitart2, author = "Guitart, Ren\'e", title = "On the geometry of computations ({II})", journal = cahiers, year = "1988", volume = "29", pages = "297-326", } @ARTICLE{guitartlair80, author = "Guitart, Ren\'e and Christian Lair", title = "Calcul Syntaxique des Mod\`eles et Calcul des Formules Internes", journal = diagrammes, year = "1980", volume = "4", } @ARTICLE{guitartlair81, author = "Guitart, Ren\'e and Christian Lair", title = "Existence de Diagrammes Localement Libres 1", journal = diagrammes, year = "1981", volume = "6", } @ARTICLE{guitartlair82, author = "Guitart, Ren\'e and Christian Lair", title = "Existence de Diagrammes Localement Libres 2", journal = diagrammes, year = "1982", volume = "7", } @ARTICLE{guitartlairrep, author = "Guitart, Ren\'e and Christian Lair", title = "Limites et Co-limites pour Repre\-senter les For\-mu\-les", journal = diagrammes, year = "1982", volume = "7", } @ARTICLE{henry, author = "Henry, C.", title = "Sur Quel\-ques Pro\-bl\`e\-mes de Plonge\-ments en Alg\'e\-bre", journal = diagrammes, year = "1982", volume = "7", note = "Gives a syntactic condition for when a structure of one type is embedded into the structure of a ``stronger'' type that it generates", } @ARTICLE{funcsem, author = "Isbell, John", title = "General Functorial Semantics,~{I}", journal = "American Journal of Mathematics", year = "1972", volume = "94", pages = "535--596", note = "General treatment of theories, including large ones", } @ARTICLE{johnwal, author = "Johnson, Michael and R. F. C. Walters", title = "Algebra Objects and Algebra Families for Finite Limit Theories", journal = jpaa, year = "1992", volume = "83", pages = "283 -- 293", } @ARTICLE{vartop, author = "Johnstone, Peter T.", title = "When is a Variety a Topos?", journal = "Algebra Universalis", year = "1985", volume = "21", pages = "198--212", } @ARTICLE{colltop, author = "Johnstone, Peter T.", title = "Collapsed Toposes and Cartesian Closed Varieties", journal = jpaa, year = "1990", volume = "129", pages = "446--480", } @BOOK{johnstonetopos, author = "Johnstone, Peter T.", title = "Topos Theory", publisher = "Academic Press", year = "1977", } @INCOLLECTION{johnstonewraith, author = "Johnstone, Peter T. and Gavin Wraith", title = "Algebraic Theories in Toposes", pages = "141--242", editor = "Johnstone, Peter T. and Gavin Wraith", booktitle = "Indexed Categories and their Applications", series = "Lecture Notes in Mathematics", volume = "661", year = "1978", publisher = springer, } @INCOLLECTION{keane, author = "Keane, Orville", title = "Abstract {H}orn Theories", booktitle = "Model Theory and Topoi", publisher = springer, volume = "445", series = lnm, year = "1975", } @BOOK{kelly74, editor = "Kelly, G.M.", title = "Category Seminar: Proceedings Sydney Category Theory Seminar", publisher = springer, year = "1974", series = "Lecture Notes in Mathematics", volume = "420", } @ARTICLE{kelly82, author = "Kelly, G.M.", title = "A Unified Treatment of Transfinite Constructions for Free Algebras, Free Monoids, Colimits, Associated Sheaves, and So On", journal = "Bulletin of the Australian Mathematical Society", year = "1980", volume = "22", pages = "1--84", } @ARTICLE{kellyess, author = "Kelly, G.M.", title = "On the Essentially-Algebraic Theory Generated by a Sketch", journal = "Bulletin of the Australian Mathematical Society", year = "1982", volume = "26", pages = "45--56", } @ARTICLE{kellystruc, author = "Kelly, G.M.", title = "Structures Defined by Finite Limits in the Enriched Context", journal = cahiers, year = "1982", volume = "23", pages = "3--42", } @BOOKLET{kellypower, author = "Kelly, G. M. and A. J. Power", title = "Algebraic Structure in the Enriched Context", year = "1991", } @BOOK{kellyenriched, author = "Kelly, G.M.", title = "Basic Concepts of Enriched Category Theory", publisher = "Cambridge University Press", year = "1982", } @ARTICLE{laircon, author = "Lair, Christian", title = "Constructions d'esquis\-ses et Transformations Naturelles G\'en\'e\-ra\-li\-s\'ees", journal = esquisses, year = "1970", volume = "2", } @ARTICLE{lairfoncomis, author = "Lair, Christian", title = "Fonc\-teurs d'omis\-sion de Struc\-tures Alg\'e\-bri\-ques", journal = oldcahiers, year = "1971", volume = "12", pages = "447--486", } @ARTICLE{lairdual, title = "Dualit\'es pours les structures alg\'e\-bri\-ques esquis\-s\'ees", author = "Christian Lair", journal = oldcahiers, volume = "15", year = "1974", pages = "353--376", } @ARTICLE{lairetgen, title = "Etude G\'en\'e\-ral de la Cat\'e\-go\-rie des esquis\-ses", author = "Christian Lair", journal = esquisses, volume = "23", year = "1975", } @ARTICLE{lairsqt, title = "Esquis\-sa\-bi\-li\-t\'e et Tri\-pla\-bi\-li\-t\'e", author = "Christian Lair", journal = oldcahiers, volume = "16", year = "1975", } @PHDTHESIS{lairthesis, author = "Lair, Christian", title = "Th\`ese de Doctorat es Sciences", school = "Univer\-sit\'e de Amiens", year = "1977", } @ARTICLE{lairferm2, title = "Fermeture standard des cat\'e\-go\-ries al'e\-bri\-ques~{II}", author = "Christian Lair", journal = oldcahiers, volume = "18", year = "1977", pages = "3--60", } @ARTICLE{lairtripsyn, author = "Lair, Christian", title = "Condition syntaxique de tripla\-bi\-li\-t\'e d'un foncteur alg\'ebrique esquiss\'e", journal = diagrammes, year = "1979", volume = "1", } @ARTICLE{lairmodel, author = "Lair, Christian", title = "Cat\'e\-go\-ries modelables et cat\'e\-gories esquis\-sa\-bles", journal = diagrammes, year = "1981", volume = "6", } @ARTICLE{lairgalois, author = "Lair, Christian", title = "Dia\-gram\-mes Localement Libres, Extensions de Corps at Th\'e\-o\-rie de {G}alois", journal = diagrammes, year = "1983", volume = "10", } @ARTICLE{lairtrames, author = "Lair, Christian", title = "Tra\-mes et Seman\-ti\-ques Cat\'ego\-ri\-ques des Syst\`emes de Tra\-mes", journal = diagrammes, year = "1987", volume = "18", } @ARTICLE{lairdiagstruc, author = "Lair, Christian", title = "Dia\-gram\-mes Struc\-tu\-r\'es de Mo\-d\`e\-les", journal = diagrammes, year = "1987", volume = "18", } @ARTICLE{lairlax, author = "Lair, Christian", title = "Lax-colimites struc\-tur\'ees", journal = diagrammes, year = "1988", volume = "20", pages = "1-90", } @INCOLLECTION{lambekscott84, author = "Lambek, Joachim and P. Scott", title = "Aspects of Higher Order Categorical Logic", pages = "145--174", editor = "Gray, J.W.", booktitle = "Mathematical Applications of Category Theory", series = "Contemporary Mathematics", publisher = ams, volume = "30", year = "1984", } @BOOK{lambekscottbook, author = "Lambek, Joachim and P. Scott", title = "Introduction to Higher Order Categorical Logic", publisher = "Cambridge University Press", series = "Cambridge Studies in Advanced Mathematics", volume = "7", year = "1986", } @PHDTHESIS{lawverefuncsem, author = "Lawvere, F.W.", title = " Functorial Semantics of Algebraic Theories", school = "Columbia University", year = "1963", } @INPROCEEDINGS{lawvere66, author = "Lawvere, F.W.", title = "The category of categories as a foundations for mathematics", booktitle = "Proceedings of the Conference on Categorial Algebra at La Jolla", publisher = springer, year = "1966", } @INPROCEEDINGS{lawvere68, author = "Lawvere, F.W.", title = "Some algebraic problems in the context of functorial semantics of algebraic structures", booktitle = "Reports of the Midwest Category Seminar~{II}", publisher = springer, series = lnm, volume = "61", year = "1968", } @PROCEEDINGS{modthtop, title = "Model Theory and Topoi", editor = "Lawvere, F.W. and C. Maurer and G. C. Wraith", series = lnm, publisher = springer, volume = "445", year = "1975", } @INPROCEEDINGS{lawvintro, author = "Lawvere, F.W.", title = "Introduction to Part~{I}", booktitle = "Model Theory and Topoi", editor = "Lawvere, F.W. and C. Maurer and G. C. Wraith", series = lnm, publisher = springer, volume = "445", year = "1975", pages = "3--14", } @INPROCEEDINGS{lawvere89, author = "Lawvere, F.W.", title = "Qualitative Distinctions Between some Toposes of Generalized Graphs", booktitle = "Categories in Computer Science and Logic", publisher = ams, volume = "92", year = "1989", } @ARTICLE{lell, author = "Lellahi, S. K.", title = "Categorical Abstract Data Types", journal = diagrammes, volume = "21", year = "1989", pages = "1--23", } @ARTICLE{lindner, author = "Lindner, Harold", title = "Morita Equivalence of Enriched Categories", journal = oldcahiers, year = "1974", volume = "15", } @INPROCEEDINGS{linton66, author = "Linton, F.E.J", title = "Some Aspects of Equational Categories", editor = "Eilenberg, S. and others", booktitle = "Proceedings of the Conference on Categorical Algebra at La Jolla", publisher = springer, year = "1966", } @INCOLLECTION{lintonoutline, author = "Linton, F.E.J.", title = "An Outline of Functional Semantics", pages = "7--52", booktitle = "Seminar on Triples and Categorical Homology Theory", series = "Lecture Notes in Mathematics", volume = "80", year = "1969", publisher = springer, } @INCOLLECTION{lintonapplied, author = "Linton, F.E.J.", title = "Applied Functorial Semantics", pages = "53--74", booktitle = "Seminar on Triples and Categorical Homology Theory", series = "Lecture Notes in Mathematics", volume = "80", year = "1969", publisher = springer, } @ARTICLE{macst2, author = "McDonald, J. and A. Stone", title = "Topoi over graphs", journal = oldcahiers, year = "1984", volume = "XXV", } @ARTICLE{macst, author = "MacDonald, John L. and Arthur Stone", title = "Uniformly Constructive Monads", journal = jpaa, year = "1990", volume = "68", pages = "225-242", } @BOOK{cwm, author = "Mac~Lane, Saunders", title = "Categories for the Working Mathematician", publisher = springer, series = "Graduate Texts in Mathematics", volume = "5", year = "1971", } @BOOK{macmoer, author = "Mac~Lane, Saunders and Ieke Moerdijk", title = "Sheaves in Geometry and Logic", publisher = springer, series = "Universitext", year = "1992", } @BOOK{mainmisloveschmidt, editor = "Main, Michael and A. Melton and Michael Mislove and D. 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Par\'e", title = "Accessible Categories: the Foundations of Categorical Model Theory", series = "Contemporary Mathematics", volume = "104", year = "1990", publisher = "American Mathematical Society", } @BOOK{makkaireyes, author = "Makkai, Michael and Gonzalo Reyes", title = "First Order Categorical Logic", publisher = springer, series = "Lecture Notes in Mathematics", volume = "611", year = "1977", } @BOOK{manesalgth, author = "Manes, E.", title = "Algebraic Theories", publisher = springer, series = "Graduate Texts in Mathematics", volume = "26", year = "1975", } @BOOK{manesarbib, author = "Manes, E. and M. Arbib", title = "Algebraic Approaches to Program Semantics", publisher = springer, year = "1986", } @BOOKLET{mckequiv, author = "McKenzie, Ralph", title = "Algebraic and Categorical Characterizations of Categorical Equivalence Between Varieties", note = "Preprint, Department of Mathematics, University of California, Berkeley, CA 94720", year = "1992", } @ARTICLE{mclartyleftexact, author = "McLarty, Colin", title = "Left Exact Logic", journal = "J. Pure Applied Algebra", year = "1986", volume = "41", pages = "63--66", } @ARTICLE{mclartyreview, author = "McLarty, Colin", title = "Review of \protect\cite{bell88}", journal = "Notre Dame Journal of Formal Logic", year = "1990", volume = "31", pages = "151--161", note = "Nice overview of toposes", } @BOOK{mclartytopos, author = "McLarty, Colin", title = "Elementary Categories, Elementary Toposes", publisher = "Clarendon Press", year = "1992", series = "Oxford Logic Guides", } @ARTICLE{mclartyfs, author = "McLarty, Colin", title = "Stable surjection logic", journal = diagrammes, year = "1989", volume = "22", pages = "45--57", } @INCOLLECTION{meseguergoguen, author = "Meseguer, J. and Joseph Goguen", title = "Initiality, Induction and Computability", editor = "Nivat, M. and J.C. 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Box~137, 00-950 Warsaw, Poland", year = "1992", } @INCOLLECTION{osius75, author = "Osius, Gerhard", title = "A Note on {K}ripke-{J}oyal Semantics for the Internal Language of Topoi", booktitle = "Model Theory and Topoi", editor = "Lawvere, F.W. and C. Maurer and G. C. Wraith", series = lnm, publisher = springer, volume = "445", pages = "349--354", year = "1975", } @INCOLLECTION{osiuslog, author = "Osius, Gerhard", title = "Logical and Set Theoretical Tools in Elementary Topoi", booktitle = "Model Theory and Topoi", editor = "Lawvere, F.W. and C. Maurer and G. C. Wraith", series = lnm, publisher = springer, volume = "445", pages = "297--346", year = "1975", } @INCOLLECTION{pareapp, title = "Some Applications of Categorical Model Theory", author = "Robert Par\'e", booktitle = "Categories in Computer Science and Logic", series = "Contemporary Mathematics", volume = "92", year = "1989", publisher = ams, pages = "325--340", } @BOOK{pareigis, author = "Pareigis, B.", title = "Categories and functors", publisher = "Academic Press", year = "1970", } @ARTICLE{peakpet, author = "Peake, E. James and Galen R. Peters", title = "Extension of Algebraic Theories", journal = "Proceedings of the American Mathematical Society", volume = 32, year = "1972", pages = "358--362", } @ARTICLE{permwall, author = "Permvall, Oskar", title = "A Bibliography on Sketches from the Computer Science Point of View", journal = "Bulletin of the European Association for Theoretical Computer Science", volume = 45, year = "1991", pages = "238--255", } @BOOKLET{phoatopos, author = "Phoa, Wesley", title = "An introduction to fibrations, topos theory, the effective topos and modest sets", howpublished = "Available by anonymous FTP from {\tt maths.su.oz.au} in the directory {\tt sydcat/papers/phoa}. It is the file {\tt tech.ps.Z}.", year = "1993", } @ARTICLE{pittsconcep, author = "Pitts, Andrew M.", title = "Conceptual Completeness for First-Order Intuitionistic Logic: An Application of Categorical Logic", pages = "33--81", volume = "41", year = "1989", journal = "Annals of Pure and Applied Logic", } @INCOLLECTION{poiprodcoprod, author = "Poign\'e, A.", title = "Elements of Categorical Reasoning: Products and Coproducts and Some other (Co-)limits", pages = "16--42", editor = "Pitt, D. and others", booktitle = "Category Theory and Computer Programming", series = "Lecture Notes in Computer Science", volume = "240", year = "1986", publisher = springer, } @INCOLLECTION{poilogic, author = "Poign\'e, A.", title = "Category Theory and Logic", pages = "103--142", editor = "Pitt, D. and others", booktitle = "Category Theory and Computer Programming", series = "Lecture Notes in Computer Science", volume = "240", year = "1986", publisher = springer, } @ARTICLE{powerwells, author = "Power, A.J. and Charles Wells", title = "A Formalism for the Specification of Essentially Algebraic Structures in 2-Categories", journal = "Mathematical Structures in Computer Science", Volume = "2", year = "1992", pages = "1--28", } @BOOK{reichel, author = "Reichel, Horst", title = "Initial Computability, Algebraic Specifications and Partial Algebras", publisher = "Clarendon Press", year = "1987", } @ARTICLE{reyessheav, author = "Reyes, Gonzalo", title = "Sheaves and Concepts: A Model-Theoretic Interpretation of {G}rothendieck Topoi", journal = oldcahiers, year = "1977", volume = "18", pages = "405--437", } @ARTICLE{rosebrughalgs, author = "Rosebrugh, Robert", title = "On Algebras Defined by Operations and Equations in a Topos", journal = "J. Pure Applied Algebra", year = "1980", volume = "17", } @INCOLLECTION{tierney76, author = "Tierney, Myles", title = "Forcing topologies and classifying topoi", publisher = "Academic Press", booktitle = "Algebra, Topology and Category Theory", editor = "Heller, Alex and Myles Tierney", year = "1976", pages = "211--220", } @INCOLLECTION{ulmer71, author = "Ulmer, Friedrich", title = "Locally $\alpha$-presentable and Locally $\alpha$-generated Categories", publisher = springer, series = lnm, booktitle = "Reports of the Midwest Category Seminar V", editor = "Gray, John W. and Saunders Mac~Lane", volume = "195", year = "1971", note = "Summary in English of results in \cite{gabrielulmer}.", } @BOOKLET{vikgeom, author = "Steve Vickers", title = "Geometric Logic in Computer Science", year = "1993", howpublished = "Available by anonymous FTP from {\tt theory.doc.ic.ac.uk} in directory {\tt papers/Vickers}. The paper is called {\tt GLiCS.dvi}.", } @INCOLLECTION{wagbloothatch, author = "Wagner, E.G. and S. Bloom and J.W. Thatcher", title = "Why Algebraic Theories?", editor = "Nivat, M. and J.C. Reynolds", booktitle = "Algebraic Methods in Semantics", year = "1985", publisher = "Cambridge University Press", } @TECHREPORT{waltnote, author = "R. F. C. Walters", title = "A Note on Context-Free Languages", institution = "The University of Sydney", number = "88-22", year = "1988", } @ARTICLE{gensk, author = "Wells, Charles", title = "A Generalization of the Concept of Sketch", journal = TCS, year = "1990", volume = "70", pages = "159--178", } @INCOLLECTION{wellsbarr, author = "Wells, Charles and M. Barr", title = "The Formal Description of Data Types using Sketches", editor = "Main, Michael and others", booktitle = "Mathematical Foundations of Programming Language Semantics", series = "Lecture Notes in Computer Science", volume = "298", year = "1988", publisher = springer, }