Please inform us of any inaccuracies or missing works.
| Title | Source | Year |
|---|---|---|
| The Language of Algebra: Supplement | TEMAC programmed learning materials | 1961 |
| The Category of Probabilistic Mappings – With Applications to Stochastic Processes, Statistics, and Pattern Recognition | Unpublished; seminar handout notes | 1962 |
| Functorial Semantics of Algebraic Theories | Original unpublished; Ph.D. thesis, Columbia University, 1963. See extended TAC reprint 2004 | 1963 |
| Functorial Semantics of Algebraic Theories (short notice) | Proceedings of the National Academy of Science 50, No. 5 (November 1963), 869-872 | 1963 |
| Functorial Automata Theory (abstract) | AMS Notices 603-151, vol 10 (1963), 477-478 | 1963 |
| The group ring of a small category (abstract) | Notices Amer. Math. Soc., 10, 280 (1963); Errata, Notices Amer. Math. Soc., 10, 516 | 1963 |
| An Elementary Theory of the Category of Sets (cf. 2005 long version with commentary) | Proceedings of the National Academy of Science 52, No. 6 (December 1964), 1506-1511 | 1964 |
| Algebraic Theories, Algebraic Categories, and Algebraic Functors | Theory of Models; North-Holland, Amsterdam (1965), 413-418 | 1965 |
| Functorial Semantics of Elementary Theories (abstract) | J. Symb. Logic, 31, 294-295, 1966 | 1966 |
| The Category of Categories as a Foundation for Mathematics | La Jolla Conference on Categorical Algebra, Springer-Verlag (1966), 1-20 | 1966 |
| Presentations of right complete categories (abstract, followed Anders Kock's notes) | Oberwolfach meeting on category theory | 1966 |
| Theories as Categories and the Completeness Theorem (abstract) | Journal of Symbolic Logic, 32:562 | 1967 |
| Some Algebraic Problems in the Context of Functorial Semantic of Algebraic Theories | Springer Lecture Notes in Mathematics No. 61 (Reports of the Midwest Category Seminar II), Springer-Verlag (1968), 41-61 | 1968 |
| Ordinal Sums and Equational Doctrines | Springer Lecture Notes in Mathematics No. 80, Springer-Verlag, 141-155. | 1969 |
| Diagonal Arguments and Cartesian Closed Categories | Springer Lecture Notes in Mathematics No. 92, Springer-Verlag (1969), 134-145. | 1969 |
| Adjointness in Foundations | Dialectica 23 (1969), 281-296 | 1969 |
| Equality in Hyperdoctrines and Comprehension Schema as an Adjoint Functor | Proceedings of the American Mathematical Society Symposium on Pure Mathematics XVII (1970), 1-14 | 1970 |
| Quantifiers and Sheaves | Proceedings of the International Congress on Mathematics, Nice 1970, Gauthier-Villars (1971) 329-334 | 1970 |
| Introduction to "Toposes, Algebraic Geometry and Logic" | Springer Lecture Notes in Mathematics No. 274, New York: Springer, pp. 1–12 | 1971 |
| Closed categories and biclosed bicategories | Mathematics Institute Aarhus Universitet, Aarhus. Handwritten lecture notes | 1971 |
| Theory of Categories over a Base Topos | Lectures given at Università di Perugia | 1972 |
| Metric Spaces, Generalized Logic, and Closed Categories | Originally published in Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 135-166; Republished in Reprints in TAC, No.1 2002 pp. 1-37 | 1973 |
| Logic of Topoi: inside and outside | Lecture Notes, Université de Montréal | 1974 |
| Introduction to "Model Theory & Topoi" | Springer Lecture Notes in Mathematics No. 445, Springer-Verlag, pp. 3-14 | 1975 |
| Variable Sets Etendu and Variable Structure in Topoi | Notes by Steven Landsburg of Lectures and Conversations, Spring 1975, University of Chicago | 1975 |
| Continuously Variable Sets – Algebraic Geometry=Geometric Logic | Studies in Logic and the Foundations of Mathematics, Volume 80, pp. 135-156 | 1975 |
| Variable Quantities and Variable Structures in Topoi | Algebra, topology, and category theory (a collection of papers in honor of Samuel Eilenberg), pp. 101–131 | 1976 |
| Discussion on philosophy (notes) | Notes by Anders Kock, Aarhus Open House, May 1978 | 1978 |
| Discussion on geometry (notes) | Notes by Anders Kock, Aarhus Open House, May 1978 | 1978 |
| Hardy fields (notes) | Notes by Anders Kock, Aarhus Open House, May 1978 | 1978 |
| Categorical Dynamics | Proceedings of Aarhus May 1978 Open House on Topos Theoretic Methods in Geometry | 1978 |
| Toward the Description in a Smooth Topos of the Dynamically Possible Motions and Deformations of a Continuous Body | Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume: 21, Issue: 4, pp. 377-392 | 1980 |
| On C-∞ functions | Preprint, State Univ. of New York, Buffalo | 1981 |
| Thermodynamics of deformations of continuous bodies, non homogeneous, with memory, far from equilibrium | Handwritten notes (in Italian) from a seminar held in Trieste | 1982 |
| Review of Cohn, Universal Algebra (second edition) | American Scientist | 1982 |
| Introduction to "Categories in Continuum Physics" | Springer Lecture Notes in Mathematics No. 1174, Springer-Verlag (1986) | 1982 |
| Measures on toposes | Proceedings of Aarhus Workshop on Category Theoretic Methods in Geometry | 1983 |
| Functorial Remarks on the General Concept of Chaos | IMA Research Report #87, University of Minnesota (1986) | 1984 |
| State Categories Closed Categories and the Existence of Semi-continuous Entropy Functions | IMA Research Report #86, University of Minnesota | 1984 |
| State Categories and Response Functors | Preprint | 1986 |
| Categories of Spaces may not be Generalized Spaces as Exemplified by Directed Graphs | Revista Colombiana de Matemáticas XX (1986), pp. 179-185 | 1986 |
| Taking Categories Seriously | Revista Colombiana de Matemáticas XX (1986), pp. 147-178 | 1986 |
| Some "New" Mathematics Arising From the Study of Grassmann 1844 | Unpublished manuscript | 1987 |
| Concepts and Problems in Mathematical Toposes (abstract) | CMS Winter Meeting, December 1988, Toronto, Program p. 31, Special Session on Category Theory | 1988 |
| Fractional Exponents in Cartesian Closed Categories | Unpublished manuscript | 1988 |
| Möbius algebra of a category | Handwritten Notes by S. Schanuel at the Sydney Combinatorics Seminar organized by Don Taylor | 1988 |
| Toposes generated by codiscrete objects in combinatorial topology and functional analysis | TAC Reprint (2021) of notes for Colloquium lectures given at North Ryde, New South Wales, Australia 1988-89 | 1989 |
| On the Complete Lattice of Essential Localizations (with G.M. Kelly) | Bull. Société Mathematique de Belgique, XLI, 289-319 | 1988 |
| Intrinsic boundary in certain mathematical toposes exemplify logical operators not passively preserved by substitution | Preprint, Univ. of Buffalo | 1989 |
| Display of Graphics and their Applications Exemplifed by 2 Categories and the Hegelian Taco | Proceedings of the First International Conference on Algebraic Methodology and Software Technology, The University of Iowa, 51-75 | 1989 |
| Qualitative Distinctions Between Some Toposes of Generalized Graphs | Proceedings of AMS Boulder 1987 Symposium on Category Theory and Computer Science, Contemporary Mathematics, 261-299 | 1989 |
| Intrinsic Co-Heyting Boundaries and the Leibniz Rule in Certain Toposes | Category Theory, Proceedings Como 1990, A. Carboni, M. C. Pedicchio, G. Rosolini (Eds). Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) pp. 279-281 | 1991 |
| More on Graphic Toposes | Proceedings of the 1989 Bangor Category Theory Meeting, Cahiers de Topologie et Géométrie Différentielle Catégorique XXXII - 1 (1991), pp. 5-10 | 1991 |
| Some Thoughts on the Future of Category Theory | Category Theory, Proceedings Como 1990. A. Carboni, M. C. Pedicchio, G. Rosolini (Eds). Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) pp. 1-13 | 1991 |
| Categories of Space and Quantity | The Space of Mathematics: Philosophical, Epistemological and Historical Explorations, International Symposium on Structures in Mathematical Theories (1990), San Sebastian, Spain; DeGruyter, Berlin (1992), pp. 14-30. | 1992 |
| Introduction to Linear Categories and Applications | Course lecture notes | 1992 |
| Cohesive Toposes and Cantor's Lauter Einsen | Philosophia Mathematica, The Canadian Society for History and Philosophy of Mathematics, Series III, Vol. 2 (1994), pp. 5-15. | 1994 |
| Tools for the Advancement of Objective Logic Closed Categories and Toposes | The Logical Foundations of Cognition, J. Macnamara, G. E. Reyes (Eds). Oxford University Press (1994), pp. 43-56 | 1994 |
| Adjoints in and among Bicategories | Logic & Algebra, Proceedings of the 1994 Siena Conference in Memory of Roberto Magari. Lecture Notes in Pure and Applied Algebra 180: pp. 181-189, Ed. Ursini/Aglianò, Marcel Dekker, Inc. Basel, New York | 1996 |
| Grassmann's Dialectics and Category Theory | Hermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar pp. 255-264, Boston Studies in the Philosophy of Science Series (BSPS, volume 187) | 1996 |
| Unity and Identity of Opposites in Calculus and Physics | Proceedings of ECCT 1994 Tours Conference, Applied Categorical Structures, 4: pp. 167-174 Kluwer Academic Publishers | 1996 |
| History and Philosophy of Mathematic Reform | CPCML Inter-Disciplinary Conference, University of Windsor on 'The Origin of Consciousness and Social Change' | 1996 |
| Algebra Step by Step | Buffalo Workshop Press, ISBN: 0963180525 | 1997 |
| Conceptual Mathematics (First Edition) | Book with Stephen Schanuel. See Second Edition, 2009 | 1997 |
| Linearization Revisited (Talk) | IIIrd Joint Meeting AMS-SMM, Special Session on Rings and Category Theory, Oaxaca Mexico, December 1997, Program p. 59 | 1997 |
| Toposes of Laws of Motion | Transcript from Video, Montreal September 27, 1997 | 1997 |
| Volterra's Functionals and Covariant Cohesion of Space | Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 64, R. Betti, F. W. Lawvere (Eds.), (2000), pp. 201-214 | 1997 |
| Everyday physics of extended bodies or why functionals need analyzing (abstract, cf. paper 2017) | Public Lecture, CMS Summer 1998 Meeting, University of New Brunswick, Saint John, June 13-15, (received May 1998) | 1998 |
| Outline of Synthetic Differential Geometry | Buffalo Geometry Seminar notes, February 1998 | 1998 |
| Are Homotopy Types the Same As Infinitesimal Skeleta? (talk, abstract) | CMS Summer 1998 Meeting | 1998 |
| Categorical Analyses of the Whole/Part Relation (abstract) | Mitteleuropaeisches Kulturinstitut, Bolzano, Italy | 1998 |
| Smoothness of Cubical Splines (Talk) | AMS Special Session on Smooth Categories in Geometry and Mechanics | 1999 |
| Categorie e Spazio: Un Profilo | Lettera matematica PRISTEM 31, Springer, Italy, (1999), 35-50. [Reprinted in La Mathematica a cura di Bartocci, Claudio, Giulio Einaudi editore (2010) vol. 4, 107-135. | 1999 |
| Kinship and Mathematical Categories | Language, Logic, and Conceptual Representation, P. Bloom, R. Jackendoff, and K. Wynn (Eds), MIT Press, (1999), pp. 411-425 | 1999 |
| Comments on the Development of Topos Theory | Development of Mathematics 1950-2000, J.-P. Pier (Ed) Birkhäuser Verlag, Basel, (2000), pp. 715-734 | 2000 |
| The Role of Cartesian Closed Categories in Foundations (Interview with Felice Cardone) | 2000 | |
| Explicit foundational concepts in the teaching of mathematics | Matematica e filosofia: il problema dei fondamenti oggi PRISTEM/Storia 14-15 - Translation: Filsofia, scienza e bioetica nel dibattito contemporaneo a cura di Minazzi, Fabio, Instituto Poligrafico e Zecca dello Stato, Roma | 2001 |
| Categorical Algebra for Continuum Micro Physics | Journal of Pure and Applied algebra 175, (2002), pp. 267-287 | 2001 |
| Incontro con Ludovico Geymonat Anno 1977 | Fabio Minazzi (ed.), Filosofia, scienza e vita civile nel pensiero di Ludovico Geymonat, La Città del Sole Napoli 2003. pp.181-185 | 2003 |
| Sets for Mathematics | Book with Robert Rosebrugh | 2003 |
| On the Duality Between Varietes and Algebraic Theories (with J. Adámek & J. Rosický) | Algebra Universalis, (2003), pp. 35-49 | 2003 |
| How Algebraic is Algebra? (with J. Adámek & J. Rosický) | Theory and Applications of Categories , Vol. 11, 2003, No. 11, pp. 252-282 | 2001 |
| Linearization of Graphic Toposes via Coxeter Groups | Journal of Pure and Applied Algebra, vol. 168, (2002), pp. 425-436 | 2002 |
| Foundations and Applications – Axiomatization and Education | The Bulletin of Symbolic Logic, vol. 9, No. 2, (2003), pp. 213-224 | 2003 |
| Continuous Categories Revisited (with J. Adámek & J. Rosický) | Theory and Applications of Categories , Vol. 11, 2003, No. 11, pp 252-282 | 2003 |
| Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories | Reprints in Theory and Applications of Categories, No. 5 (2004) pp 1-121. Originally published as: Ph.D. thesis, Columbia University, 1963 and in Reports of the Midwest Category Seminar II, 1968, pp. 41-61 | 2004 |
| Functorial Concepts of Complexity for Finite Automata | Theory and Applications of Categories, Vol. 13, 2004, No. 10, pp. 164-168 | 2004 |
| Left and Right Adjoint Operations on Spaces and Data Types | For Dana Scott's Seventieth Birthday, Copenhagen 2002, Theoretical Computer Science, Elsevier, vol 316/1-3, (2004) pp. 105-111 | 2004 |
| An Elementary Theory of the Category of Sets (long version) with commentary | Reprints in Theory and Applications of Categories, No. 11 (2005) pp. 1-35. Expanded version of Proceedings of the National Academy of Science of the U.S.A 52, 1506-1511, with commentary by Colin McLarty and the author. | 2005 |
| Grassmann Book Reviews | Historia Mathematica, vol. 32, (2005), pp. 101-106 | 2005 |
| John Isbell's Adequate Subcategories | Topological Commentary, Vol. 11 #1 | 2006 |
| Review of Anders Kock, Synthetic Differential Geometry (second edition) | SIAM review | 2007 |
| Axiomatic Cohesion | Theory and Applications of Categories, online publication, Special volume from the CT2006 Conference at Whitepoint Nova Scotia, vol 19, (2007), 41-49 | 2007 |
| Cohesive toposes: combinatorial and infinitesimal cases (video) (lecture notes) | Lectures in Como (Italy), January 10, 2008 | 2008 |
| Core Varieties Extensivity and Rig Geometry | Theory and Applications of Categories, Vol. 20, 2008, No. 14, pp 497-503. | 2008 |
| Interview with Maria Manuel Clementino and Jorge Picado | Bulletin of the International Center for Mathematics (part 1, December 2007, part 2, June 2008) | 2008 |
| Foreword To "Algebraic Theories" | Cambridge Tracts in Mathematics 184, J. Adámek, J. Rosický & E. M. Vitale (2012) | 2009 |
| Conceptual Mathematics (Second Edition) | Book with Stephen Schanuel | 2009 |
| Open Problems in Topos Theory | 88th Peripatetic Seminar on Sheaves and Logic, For Martin Hyland and Peter Johnstone in honor of their sixtieth birthdays (updated July 2016) | 2009 |
| The Hopf Algebra of Möbius Intervals (with M. Menni) | Theory and Applications of Categories, online publication, vol. 24, (2010), 221-265 | 2010 |
| Categorical Dynamics (abstract) | Talk at International Category Theory Conference, Vancouver, July 2011 | 2011 |
| Euler's Continuum Functorially Vindicated | Logic, Mathematics, Philosophy: Vintage Enthusiasms, Essays in Honour of John L. Bell, D. DeVidi et al. (Eds), Western Ontario Series in Philosophy of Science 75, (2011) | 2011 |
| What Is A Space? (video) | Sets Within Geometry symposium - Nancy, France 26-29 July 2011 | 2011 |
| The Dialectic of Continuous and Discrete in the History of the Struggle for a Usable Guide to Mathematical Thought (video) | Sets Within Geometry symposium - Nancy, France 26-29 July 2011 | 2011 |
| Categorical Dynamics Revisited: Category Theory and the Representation of Physical Quantities (video) | Sets Within Geometry symposium - Nancy, France 26-29 July 2011 | 2011 |
| What are Foundations of Geometry and Algebra? (abstract (video) (transcript) | Fifty Years of Functorial Semantics Conference | 2013 |
| Internal Choice Holds in the Discrete Part of any Cohesive Topos Satisfying Stable Connected Codiscreteness (with M. Menni) | Theory and Applications of Categories, online publication, vol. 30, (2015), No. 26, pp 909-932 | 2015 |
| Alexander Grothendieck and the Concept of Space | Invited address at CT 2015 Aveiro, Portugal | 2015 |
| Birkhoff's Theorem from a Geometric Perspective: A Simple Example | Categories and General Algebraic Structures with Apllications Vol. 4, no. 1, (2016), pp. 1-7 | 2016 |
| Everyday physics of extended bodies or why functionals need analyzing | Categories and General Algebraic Structures with Applications, Volume 6 2017, pp. 9-19 | 2017 |