The collected works of F. W. Lawvere
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pdfs add categorical dynamics 1978 Aug 24, 2017
README.md ordering Aug 26, 2017

README.md

The collected works of F. W. Lawvere

Please inform us of any inaccuracies or missing works.

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The Category of Probabilistic Mappings – With Applications to Stochastic Processes, Statistics, and Pattern Recognition Unpublished; seminar handout notes 1962
Functorial Semantics of Algebraic Theories Original unpublished; Ph.D. thesis, Columbia University, 1963.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
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