The collected works of F. W. Lawvere

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| Title |Source| Year | |:------|:-----|:----:| |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Category of Probabilistic Mappings – With Applications to Stochastic Processes, Statistics, and Pattern Recognition|Unpublished; seminar handout notes|1962| |Functorial Semantics of Algebraic Theories|Original unpublished; Ph.D. thesis, Columbia University, 1963.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| |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| |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| |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 from a seminar held in Trieste|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|Notes for Colloquium lectures given at North Ryde, New South Wales, Australia on April|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| |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| |Algebra Step by Step|Buffalo Workshop Press, ISBN: 0963180525|1997| |Linearization Revisited (abstract)|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? (abstract)|CMS Summer 1998 Meeting|1998| |Categorical Analyses of the Whole/Part Relation (abstract)|Mitteleuropaeisches Kulturinstitut, Bolzano, Italy|1998| |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| |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| |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| |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|