Lawvere

F. William Lawvere
Ramifications of Category Theory (Firenze, November 2003)
Born	(1937-02-09) February 9, 1937 (age 80) Muncie, Indiana
Nationality	United States
Fields	Mathematics
Institutions	SUNY-Buffalo
Alma mater	Columbia University
Doctoral advisor	Samuel Eilenberg
Doctoral students	Marta Bunge Emilio Faro-Rivas Anders Kock Xiao-Qing Meng Philip Mulry Jack Reichman Kimmo Rosenthal Michael Roy Michel Thiébaud
Known for	Contributions to topos theory and philosophy of mathematics Lawvere theory
Notable awards	Premio Giulio Preti, awarded by the Consiglio regionale della Toscana in 2010

Francis William Lawvere (/ˈlɔːvɪər/; born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.

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.

Before completing the Ph.D. Lawvere spent a year in Berkeley as an informal student of model theory and set theory, following lectures by Alfred Tarski and Dana Scott. In his first teaching position at Reed College he was instructed to devise courses in calculus and abstract algebra from a foundational perspective. He tried to use the then current axiomatic set theory but found it unworkable for undergraduates, so he instead developed the first axioms for the more relevant composition of mappings of sets. He later streamlined those axioms into the Elementary Theory of the Category of Sets (1964) (Reprints, #11) which became a key ingredient (the constant case) of elementary topos theory.