#6,421

Most Influential Person

American mathematician

According to Wikipedia, Francis William Lawvere is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics. Biography Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell. He learned of category theory while teaching a course on functional analysis for Truesdell, specifically from a problem in John L. Kelley's textbook General Topology. Lawvere found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll. Truesdell supported Lawvere's application to study further with Samuel Eilenberg, a founder of category theory, at Columbia University in 1960.

- FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES. (1963) (918)
- Metric spaces, generalized logic, and closed categories (1973) (707)
- Adjointness in Foundations (1969) (375)
- AN ELEMENTARY THEORY OF THE CATEGORY OF SETS. (1964) (361)
- Conceptual mathematics - a first introduction to categories (1997) (337)
- The Category of Categories as a Foundation for Mathematics (1966) (212)
- Sets for Mathematics (2003) (190)
- Some algebraic problems in the context of functorial semantics of algebraic theories (1968) (189)
- Diagonal arguments and cartesian closed categories (1969) (144)
- Toposes, Algebraic Geometry and Logic (1972) (120)
- Ordinal sums and equational doctrines (1969) (97)
- Category Theory, Homology Theory and their Applications II (1969) (82)
- Continuously Variable Sets; Algebraic Geometry = Geometric Logic (1975) (74)
- Some thoughts on the future of category theory (1991) (73)
- Taking categories seriously (1986) (72)
- Variable Quantities and Variable Structures in Topoi (1976) (56)
- Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes (1991) (52)
- AXIOMATIC COHESION (2007) (51)
- Cohesive Toposes and Cantor's 'lauter Einsen' (1994) (49)
- Categories of Space and of Quantity (1992) (47)
- Qualitative distinctions between some toposes of generalized graphs (1987) (46)
- QUANTIFIERS AND SHEAVES by (2010) (45)
- Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body (1980) (44)
- THE HOPF ALGEBRA OF MÖBIUS INTERVALS (2010) (34)
- On the duality between varieties and algebraic theories (2003) (32)
- Categories of spaces may not be generalized spaces as exemplified by directed graphs (1986) (29)
- Foundations and Applications: Axiomatization and Education (2003) (29)
- Unity and identity of opposites in calculus and physics (1996) (24)
- COMBINATORICS OF CURVATURE, AND THE BIANCHI IDENTITY (1996) (23)
- Model Theory and Topoi (1975) (21)
- Categories in continuum physics : lectures given at a workshop held at SUNY, Buffalo, 1982 (1986) (21)
- HOW ALGEBRAIC IS ALGEBRA (2001) (17)
- INTERNAL CHOICE HOLDS IN THE DISCRETE PART OF ANY COHESIVE TOPOS SATISFYING STABLE CONNECTED CODISCRETENESS We dedicate this paper to the memory of our friend R.F.C.Walters. (2015) (16)
- Comments on the Development of Topos Theory (2000) (15)
- Continuous categories revisited. (2003) (14)
- More on graphic toposes (1991) (12)
- CORE VARIETIES, EXTENSIVITY, AND RIG GEOMETRY (2008) (10)
- Categorical algebra for continuum micro physics (2002) (9)
- Conceptual Mathematics by F. William Lawvere (2009) (8)
- Volterra's functionals and covariant cohesion of space (1998) (8)
- State Categories, Closed Categories, and the Existence Semi-Continuous Entropy Functions (1984) (7)
- Variable sets etendu and variable structure in topoi (1975) (7)
- Linearization of graphic toposes via Coxeter groups (2002) (7)
- Toposes of Laws of Motion (1998) (6)
- Euler’s Continuum Functorially Vindicated (2011) (6)
- Outline of Synthetic Differential Geometry (1998) (5)
- Conceptual Mathematics: Quiz (2009) (5)
- Grassmann’s Dialectics and Category Theory (1996) (5)
- Co-existence of Krull filtrations (2001) (4)
- Birkhoff's Theorem from a geometric perspective: A simple example (2016) (3)
- Left and right adjoint operations on spaces and data types (2004) (2)
- What are Foundations of Geometry and Algebra ? (2)
- Algebraic Theories: Properties of algebras (2010) (2)
- ALGEBRAIC THEORIES, ALGEBRAIC CATEGORIES, AND ALGEBRAIC FUNCTORS (2014) (2)
- Adjoints in and among Bicategories (2017) (2)
- FUNCTORIAL CONCEPTS OF COMPLEXITY FOR FINITE AUTOMATA For Aurelio, an exacting colleague and a treasured friend since 1972, when he was one of the unfailingly enthusiastic four who traveled weekly from Milan to Perugia for mathematical discussions "fuori programma". (2004) (2)
- Conceptual Mathematics: The category of sets (2009) (2)
- Conceptual Mathematics: Universal mapping properties (2009) (2)
- Everyday physics of extended bodies or why functionals need analyzing (2017) (1)
- Model theory and topoi : a collection of lectures by various authors (1975) (1)
- Conceptual Mathematics: Products in categories (2009) (1)
- Review: History of Mathematics (2005) (1)
- Conceptual Mathematics: Isomorphisms (2009) (1)
- Algebraic Theories: Sifted and filtered colimits (2010) (1)
- Functional Remarks on the General Concept of Chaos (1984) (1)
- Sets for Mathematics: Bibliography (2003) (0)
- Conceptual Mathematics: Monoids (2009) (0)
- Conceptual Mathematics: Constants, codiscrete objects, and many connected objects (2009) (0)
- Conceptual Mathematics: Sets, maps, composition (2009) (0)
- Map object versus product (2009) (0)
- Conceptual Mathematics: Test 4 (2009) (0)
- Conceptual Mathematics: Composition of opposed maps (2009) (0)
- Conceptual Mathematics: Test 2 (2009) (0)
- Algebraic Theories: More about dualities for one-sorted algebraic categories (2010) (0)
- Algebraic Theories: One-sorted algebraic categories (2010) (0)
- Algebraic Theories: Monads (2010) (0)
- The Axiom of Choice and Maximal Principles (2003) (0)
- Algebraic Theories: Abelian categories (2010) (0)
- Algebraic Theories: Algebraic functors (2010) (0)
- Conceptual Mathematics: Review of Test 2 (2009) (0)
- Conceptual Mathematics: APPENDICES (2009) (0)
- Conceptual Mathematics: Retracts and idempotents (2009) (0)
- Finite Inverse Limits (2003) (0)
- Sets for Mathematics: Introduction to Variable Sets (2003) (0)
- Sets for Mathematics: Models of Additional Variation (2003) (0)
- Algebraic Theories: Preface (2010) (0)
- Lawvere, F.William (1986) (0)
- Algebraic Theories: Exact completion and reflexive-coequalizer completion (2010) (0)
- Conceptual Mathematics: Categories of structured sets (2009) (0)
- Algebraic Theories: Free exact categories (2010) (0)
- Conceptual Mathematics: Parts of an object: Toposes (2009) (0)
- Cohesive Toposes and Cantor ' s ' iaufcer Einsen ' (2005) (0)
- Summary/quiz on pairs of ‘opposed’ maps (2009) (0)
- Conceptual Mathematics: Two general aspects or uses of maps (2009) (0)
- Conceptual Mathematics: The algebra of composition (2009) (0)
- Conceptual Mathematics: More on universal mapping properties (2009) (0)
- Conceptual Mathematics: Composing maps and counting maps (2009) (0)
- How to solve the quiz problems (2009) (0)
- Conceptual Mathematics: Preface (2009) (0)
- Conceptual Mathematics: Organisation of the book (2009) (0)
- Conceptual Mathematics: Map objects (2009) (0)
- Sets for Mathematics: Summary of the Axioms and an Example of Variable Sets (2003) (0)
- Conceptual Mathematics: The category of pointed sets (2009) (0)
- Conceptual Mathematics: Elementary universal mapping properties (2009) (0)
- Sets for Mathematics: Sums, Monomorphisms, and Parts (2003) (0)
- Algebras for an endofunctor (2010) (0)
- Conceptual Mathematics: Terminal objects (2009) (0)
- Conceptual Mathematics: Maps preserve positive properties (2009) (0)
- A characterization of algebraic categories (2010) (0)
- Conceptual Mathematics: The Connected Components Functor (2009) (0)
- Conceptual Mathematics: Annotated Bibliography (2009) (0)
- Conceptual Mathematics: Geometery of figures and algebra of functions (2009) (0)
- Algebraic Theories: Reflexive coequalizers (2010) (0)
- Algebraic Theories: Finitary localizations of algebraic categories (2010) (0)
- Conceptual Mathematics: Division of maps: Sections and retractions (2009) (0)
- Algebraic categories as free completions (2010) (0)
- Conceptual Mathematics: Brouwer's theorems (2009) (0)
- Conceptual Mathematics: Galileo and multiplication of objects (2009) (0)
- Algebraic Theories: Equational categories of Σ-algebras (2010) (0)
- Sets for Mathematics: Definitions, Symbols, and the Greek Alphabet (2003) (0)
- Conceptual Mathematics: Ascending to categories of richer structures (2009) (0)
- Objectification of properties in dynamical systems (2009) (0)
- Sets for Mathematics: Abstract Sets and Mappings (2003) (0)
- Conceptual Mathematics: Distributive categories and linear categories (2009) (0)
- Conceptual Mathematics: Adjoint functors with examples from graphs and dynamical systems (2009) (0)
- MFCSIT 2002 : Invited Speakers 2 Constraints and Complexity : Attack of the Clones (2002) (0)
- Sets for Mathematics: Foreword (2003) (0)
- Algebraic Theories: Birkhoff's variety theorem (2010) (0)
- Conceptual Mathematics: Points of an object (2009) (0)
- Conceptual Mathematics: Some uses of graphs (2009) (0)
- Conceptual Mathematics: Test 5 (2009) (0)
- Conceptual Mathematics: Test 1 (2009) (0)
- Conceptual Mathematics: Pictures of a map making its features evident (2009) (0)
- Algebraic Theories: Canonical theories (2010) (0)
- Sets, maps, and composition (2009) (0)
- Algebraic Theories: References (2010) (0)
- Conceptual Mathematics: Higher universal mapping properties (2009) (0)
- Conceptual Mathematics: The contravariant parts functor (2009) (0)
- Sets for Mathematics: Colimits, Epimorphisms, and the Axiom of Choice (2003) (0)
- Sets for Mathematics: More on Power Sets (2003) (0)
- Algebraic Theories: Postscript (2010) (0)
- Algebraic Theories: Preliminaries (2010) (0)
- Conceptual Mathematics: Uniqueness of products and definition of sum (2009) (0)
- Logic as the Algebra of Parts (2003) (0)
- Conceptual Mathematics: Exponentiation (2009) (0)
- Conceptual Mathematics: Group theory and the number of types of connected objects (2009) (0)
- Conceptual Mathematics: Test 3 (2009) (0)
- Conceptual Mathematics: Categories of diagrams (2009) (0)
- Conceptual Mathematics: Labelings and products of graphs (2009) (0)
- Conceptual Mathematics: Idempotents, involutions, and graphs (2009) (0)
- Conceptual Mathematics: Examples of categories (2009) (0)
- Algebraic Theories: CONCRETE ALGEBRAIC CATEGORIES (2010) (0)
- Conceptual Mathematics: Binary operations and diagonal arguments (2009) (0)
- From filtered to sifted (2010) (0)
- Algebraic Theories: Algebraic theories and algebraic categories (2010) (0)
- Mapping Sets and Exponentials (2003) (0)
- Conceptual Mathematics: Examples of universal constructions (2009) (0)
- Consequences and Uses of Exponentials (2003) (0)
- Conceptual Mathematics: Universal mapping properties and incidence relations (2009) (0)
- Conceptual Mathematics: Summary: On the equation p ∘ j = 1A (2009) (0)
- Conceptual Mathematics: Review of ‘I-words’ (2009) (0)
- Some uses of graphs (2009) (0)
- Conceptual Mathematics: Isomorphisms and coordinates (2009) (0)
- Algebraic Theories: ABSTRACT ALGEBRAIC CATEGORIES (2010) (0)
- Conceptual Mathematics: The emergence of category theory within mathematics (2009) (0)
- Algebraic Theories: SPECIAL TOPICS (2010) (0)
- Conceptual Mathematics: Division of maps: Isomorphisms (2009) (0)
- Subobject, logic, and truth (2009) (0)

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