# William Lawvere

American mathematician

## William Lawvere's AcademicInfluence.com Rankings

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Mathematics

## William Lawvere's Degrees

- PhD Mathematics Columbia University

## Why Is William Lawvere Influential?

(Suggest an Edit or Addition)According to Wikipedia, Francis William Lawvere was an American 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.

## William Lawvere's Published Works

### Published Works

- FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES. (1963) (957)
- Metric spaces, generalized logic, and closed categories (1973) (758)
- Adjointness in Foundations (1969) (399)
- AN ELEMENTARY THEORY OF THE CATEGORY OF SETS. (1964) (376)
- Conceptual mathematics - a first introduction to categories (1997) (366)
- The Category of Categories as a Foundation for Mathematics (1966) (221)
- Some algebraic problems in the context of functorial semantics of algebraic theories (1968) (200)
- Sets for Mathematics (2003) (196)
- Diagonal arguments and cartesian closed categories (1969) (155)
- Toposes, Algebraic Geometry and Logic (1972) (128)
- Ordinal sums and equational doctrines (1969) (100)
- Category Theory, Homology Theory and their Applications II (1969) (94)
- Some thoughts on the future of category theory (1991) (81)
- Taking categories seriously (1986) (76)
- Continuously Variable Sets; Algebraic Geometry = Geometric Logic (1975) (76)
- AXIOMATIC COHESION (2007) (60)
- Variable Quantities and Variable Structures in Topoi (1976) (57)
- QUANTIFIERS AND SHEAVES by (2010) (54)
- Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes (1991) (54)
- Qualitative distinctions between some toposes of generalized graphs (1987) (51)
- Cohesive Toposes and Cantor's 'lauter Einsen' (1994) (50)
- Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body (1980) (49)
- Categories of Space and of Quantity (1992) (48)
- THE HOPF ALGEBRA OF MÖBIUS INTERVALS (2010) (42)
- On the duality between varieties and algebraic theories (2003) (33)
- Foundations and Applications: Axiomatization and Education (2003) (32)
- Categories of spaces may not be generalized spaces as exemplified by directed graphs (1986) (32)
- COMBINATORICS OF CURVATURE, AND THE BIANCHI IDENTITY (1996) (28)
- Unity and identity of opposites in calculus and physics (1996) (25)
- Categories in continuum physics : lectures given at a workshop held at SUNY, Buffalo, 1982 (1986) (22)
- Model Theory and Topoi (1975) (21)
- 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) (20)
- HOW ALGEBRAIC IS ALGEBRA (2001) (18)
- Comments on the Development of Topos Theory (2000) (15)
- Continuous categories revisited. (2003) (14)
- More on graphic toposes (1991) (13)
- CORE VARIETIES, EXTENSIVITY, AND RIG GEOMETRY (2008) (12)
- Volterra's functionals and covariant cohesion of space (1998) (10)
- Categorical algebra for continuum micro physics (2002) (10)
- Linearization of graphic toposes via Coxeter groups (2002) (9)
- Toposes of Laws of Motion (1998) (9)
- Conceptual Mathematics by F. William Lawvere (2009) (8)
- State Categories, Closed Categories, and the Existence Semi-Continuous Entropy Functions (1984) (8)
- Euler’s Continuum Functorially Vindicated (2011) (8)
- Variable sets etendu and variable structure in topoi (1975) (7)
- Outline of Synthetic Differential Geometry (1998) (6)
- 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)
- Functional Remarks on the General Concept of Chaos (1984) (2)
- Everyday physics of extended bodies or why functionals need analyzing (2017) (2)
- What are Foundations of Geometry and Algebra ? (2)
- Algebraic Theories: Properties of algebras (2010) (2)
- Conceptual Mathematics: Universal mapping properties (2009) (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)
- ALGEBRAIC THEORIES, ALGEBRAIC CATEGORIES, AND ALGEBRAIC FUNCTORS (2014) (2)
- Left and right adjoint operations on spaces and data types (2004) (2)
- Conceptual Mathematics: The category of sets (2009) (2)
- Algebraic Theories: Sifted and filtered colimits (2010) (1)
- Conceptual Mathematics: Products in categories (2009) (1)
- Review: History of Mathematics (2005) (1)
- Conceptual Mathematics: Isomorphisms (2009) (1)
- Conceptual Mathematics: Quiz (2009) (1)
- Adjoints in and among Bicategories (2017) (1)
- Model theory and topoi : a collection of lectures by various authors (1975) (1)
- Mapping Sets and Exponentials (2003) (0)
- Algebraic Theories: Birkhoff's variety theorem (2010) (0)
- Conceptual Mathematics: Brouwer's theorems (2009) (0)
- Conceptual Mathematics: Review of Test 2 (2009) (0)
- Conceptual Mathematics: Organisation of the book (2009) (0)
- Lawvere, F.William (1986) (0)
- Algebraic Theories: Preliminaries (2010) (0)
- Conceptual Mathematics: Higher universal mapping properties (2009) (0)
- Conceptual Mathematics: More on universal mapping properties (2009) (0)
- Algebraic Theories: Free exact categories (2010) (0)
- Algebraic Theories: Postscript (2010) (0)
- Sets for Mathematics: Introduction to Variable Sets (2003) (0)
- Some uses of graphs (2009) (0)
- Algebras for an endofunctor (2010) (0)
- Algebraic categories as free completions (2010) (0)
- Algebraic Theories: ABSTRACT ALGEBRAIC CATEGORIES (2010) (0)
- Sets for Mathematics: Abstract Sets and Mappings (2003) (0)
- Algebraic Theories: Abelian categories (2010) (0)
- Conceptual Mathematics: The algebra of composition (2009) (0)
- Conceptual Mathematics: Ascending to categories of richer structures (2009) (0)
- Conceptual Mathematics: Test 1 (2009) (0)
- Conceptual Mathematics: Universal mapping properties and incidence relations (2009) (0)
- Conceptual Mathematics: Uniqueness of products and definition of sum (2009) (0)
- Conceptual Mathematics: Maps preserve positive properties (2009) (0)
- Algebraic Theories: One-sorted algebraic categories (2010) (0)
- Algebraic Theories: More about dualities for one-sorted algebraic categories (2010) (0)
- Conceptual Mathematics: Pictures of a map making its features evident (2009) (0)
- Consequences and Uses of Exponentials (2003) (0)
- Summary/quiz on pairs of ‘opposed’ maps (2009) (0)
- A characterization of algebraic categories (2010) (0)
- Conceptual Mathematics: The contravariant parts functor (2009) (0)
- Conceptual Mathematics: Summary: On the equation p ∘ j = 1A (2009) (0)
- Conceptual Mathematics: Idempotents, involutions, and graphs (2009) (0)
- Conceptual Mathematics: Test 5 (2009) (0)
- Algebraic Theories: References (2010) (0)
- Map object versus product (2009) (0)
- Conceptual Mathematics: Terminal objects (2009) (0)
- Objectification of properties in dynamical systems (2009) (0)
- Algebraic Theories: Preface (2010) (0)
- Conceptual Mathematics: Test 4 (2009) (0)
- Sets for Mathematics: More on Power Sets (2003) (0)
- Conceptual Mathematics: The Connected Components Functor (2009) (0)
- Algebraic Theories: Algebraic theories and algebraic categories (2010) (0)
- Conceptual Mathematics: Two general aspects or uses of maps (2009) (0)
- Conceptual Mathematics: Parts of an object: Toposes (2009) (0)
- The Axiom of Choice and Maximal Principles (2003) (0)
- Conceptual Mathematics: The emergence of category theory within mathematics (2009) (0)
- Algebraic Theories: Algebraic functors (2010) (0)
- Conceptual Mathematics: Points of an object (2009) (0)
- Conceptual Mathematics: Isomorphisms and coordinates (2009) (0)
- Conceptual Mathematics: Division of maps: Isomorphisms (2009) (0)
- Conceptual Mathematics: Labelings and products of graphs (2009) (0)
- Sets for Mathematics: Foreword (2003) (0)
- MFCSIT 2002 : Invited Speakers 2 Constraints and Complexity : Attack of the Clones (2002) (0)
- Logic as the Algebra of Parts (2003) (0)
- Conceptual Mathematics: Composition of opposed maps (2009) (0)
- Conceptual Mathematics: Map objects (2009) (0)
- Subobject, logic, and truth (2009) (0)
- From filtered to sifted (2010) (0)
- Conceptual Mathematics: Composing maps and counting maps (2009) (0)
- Sets for Mathematics: Definitions, Symbols, and the Greek Alphabet (2003) (0)
- How to solve the quiz problems (2009) (0)
- Conceptual Mathematics: The category of pointed sets (2009) (0)
- Conceptual Mathematics: Distributive categories and linear categories (2009) (0)
- Algebraic Theories: Reflexive coequalizers (2010) (0)
- Algebraic Theories: Canonical theories (2010) (0)
- Algebraic Theories: Monads (2010) (0)
- Sets for Mathematics: Summary of the Axioms and an Example of Variable Sets (2003) (0)
- Conceptual Mathematics: Monoids (2009) (0)
- Conceptual Mathematics: Galileo and multiplication of objects (2009) (0)
- Sets for Mathematics: Sums, Monomorphisms, and Parts (2003) (0)
- Conceptual Mathematics: Sets, maps, composition (2009) (0)
- Algebraic Theories: CONCRETE ALGEBRAIC CATEGORIES (2010) (0)
- Conceptual Mathematics: Preface (2009) (0)
- Conceptual Mathematics: Examples of universal constructions (2009) (0)
- Conceptual Mathematics: Retracts and idempotents (2009) (0)
- Conceptual Mathematics: Elementary universal mapping properties (2009) (0)
- Conceptual Mathematics: APPENDICES (2009) (0)
- Algebraic Theories: Exact completion and reflexive-coequalizer completion (2010) (0)
- Conceptual Mathematics: Exponentiation (2009) (0)
- Conceptual Mathematics: Examples of categories (2009) (0)
- Conceptual Mathematics: Constants, codiscrete objects, and many connected objects (2009) (0)
- Sets, maps, and composition (2009) (0)
- Conceptual Mathematics: Categories of structured sets (2009) (0)
- Conceptual Mathematics: Review of ‘I-words’ (2009) (0)
- Conceptual Mathematics: Geometery of figures and algebra of functions (2009) (0)
- Conceptual Mathematics: Annotated Bibliography (2009) (0)
- Finite Inverse Limits (2003) (0)
- Conceptual Mathematics: Test 2 (2009) (0)
- Algebraic Theories: SPECIAL TOPICS (2010) (0)
- Conceptual Mathematics: Adjoint functors with examples from graphs and dynamical systems (2009) (0)
- Conceptual Mathematics: Group theory and the number of types of connected objects (2009) (0)
- Algebraic Theories: Equational categories of Σ-algebras (2010) (0)
- Sets for Mathematics: Bibliography (2003) (0)
- Conceptual Mathematics: Some uses of graphs (2009) (0)
- Conceptual Mathematics: Test 3 (2009) (0)
- Sets for Mathematics: Models of Additional Variation (2003) (0)
- Cohesive Toposes and Cantor ' s ' iaufcer Einsen ' (2005) (0)
- Sets for Mathematics: Colimits, Epimorphisms, and the Axiom of Choice (2003) (0)
- Conceptual Mathematics: Binary operations and diagonal arguments (2009) (0)
- Conceptual Mathematics: Categories of diagrams (2009) (0)
- Conceptual Mathematics: Division of maps: Sections and retractions (2009) (0)
- Algebraic Theories: Finitary localizations of algebraic categories (2010) (0)

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