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 where Kelley suggests the functorial approach "might be called the galactic theory" (p. 246) compared to the older ideas of local and global questions. 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 more pure mathematics 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) which became a key ingredient (the constant case) of elementary topos theory.
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