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The collected works of F. W. Lawvere

Please inform us of any inaccuracies or missing works.

Title Date
The Category of Probabilistic Mappings – With Applications to Stochastic Processes, Statistics, and Pattern Recognition 1962
Functorial Semantics of Algebraic Theories (original unpublished, cf. 2004) 1963
Functorial Semantics of Algebraic Theories (short notice, cf. 2004 full version) 1963
An Elementary Theory of the Category of Sets (cf. 2005 long version with commentary) 1964
Algebraic Theories, Algebraic Categories, and Algebraic Functors 1965
Category of Categories as a Foundation for Mathematics 1966
Some Algebraic Problems in the Context of Functorial Semantic of Algebraic Theories 1968
Adjointness in Foundations 1969
Diagonal Arguments and Cartesian Closed Categories 1969
Ordinal Sums and Equational Doctrines 1969
Equality in Hyperdoctrines and Comprehension Schema as an Adjoint Functor 1970
Quantifiers and Sheaves 1971
Introduction to Toposes, Algebraic Geometry and Logic (LNM 274) 1971
Theory of Categories over a Base Topos (Perugia Lecture Notes) 1972
Metric Spaces Generalized Logic Closed Categories 1973
Introduction to Model Theory & Topoi (LNM 445) 1975
Variable Sets Etendu and Variable Structure in Topoi 1975
Continuously Variable Sets – Algebraic Geometry=Geometric Logic 1975
Variable Quantities and Variable Structures in Topoi 1976
Categorical Dynamics (abstract) (missing; in 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 1980
Introduction to Categories in Continuum Physics (LNM 1174) 1982
Functorial Remarks on the General Concept of Chaos 1984
State Categories Closed Categories and the Existence of Semi-continuous Entropy Functions 1984
Categories of Spaces may not be Generalized Spaces as Exemplified by Directed Graphs 1986
Taking Categories Seriously 1986
On the Complete Lattice of Essential Localizations (with G.M. Kelly) 1988
Display of Graphics and their Applications Exemplifed by 2 Categories and the Hegelian Taco 1989
Qualitative Distinctions Between Some Toposes of Generalized Graphs 1989
Intrinsic Co-Heyting Boundaries and the Leibniz Rule in Certain Toposes 1991
More on Graphic Toposes 1991
Some Thoughts on the Future of Category Theory 1991
Categories of Space and Quantity 1992
Cohesive Toposes and Cantor's Lauter Einsen 1994
Tools for the Advancement of Objective Logic Closed Categories and Toposes 1994
Adjoints in and among Bicategories 1996
Grassmann's Dialectics and Category Theory 1996
Unity and Identity of Opposites in Calculus and Physics 1996
Toposes of Laws of Motion 1997
Volterra's Functionals and Covariant Cohesion of Space 1997
Outline of Synthetic Differential Geometry 1998
Kinship and Mathematical Categories 1999
Comments on the Development of Topos Theory 2000
The Role of Cartesian Closed Categories in Foundations (Interview with Felice Cardone) 2000
Categorical Algebra for Continuum Micro Physics 2001
How Algebraic is Algebra? (with J. Adámek & J. Rosický) 2001
Linearization of Graphic Toposes via Coxeter Groups 2002
Foundations and Applications – Axiomatization and Education 2003
Continuous Categories Revisited (with J. Adámek & J. Rosický) 2003
Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories) 2004
Functorial Concepts of Complexity for Finite Automata 2004
Left and Right Adjoint Operations on Spaces and Data Types 2004
An Elementary Theory of the Category of Sets (long version with commentary) 2005
Grassmann Book Reviews 2005
Axiomatic Cohesion 2007
Cohesive toposes: combinatorial and infinitesimal cases (video) (lecture notes) 2008
Core Varieties Extensivity and Rig Geometry 2008
Interview with Jorge Picado 2008
Open Problems in Topos Theory 2009
The Hopf Algebra of Möbius Intervals (with M. Menni) 2010
Euler's Continuum Functorially Vindicated 2011
What are Foundations of Geometry and Algebra? (abstract) (video) (transcript) 2013
Internal Choice Holds in the Discrete Part of any Cohesive Topos Satisfying Stable Connected Codiscreteness (with M. Menni) 2015
Alexander Grothendieck and the Concept of Space (address at CT15 Aveiro) 2015
Birkhoff's Theorem from a Geometric Perspective: A Simple Example 2016

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