William Lawvere

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William Lawvere
SUNY-Buffalo
Doctoral advisorSamuel Eilenberg

Francis William Lawvere (

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.[1]

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 an ingredient (the constant case) of elementary topos theory.

Lawvere died on January 23, 2023, at the age of 85.[1]

Work

Lawvere completed his

quantifiers can be characterized as special cases of adjoint functors
.

Back in Zürich for 1968–69 he proposed elementary (first-order) axioms for toposes generalizing the concept of the Grothendieck topos (see history of topos theory) and worked with the algebraic topologist Myles Tierney to clarify and apply this theory. Tierney discovered major simplifications in the description of Grothendieck "topologies". Anders Kock later found further simplifications so that a topos can be described as a category with products and equalizers in which the notions of map space and subobject are representable. Lawvere had pointed out that a Grothendieck topology can be entirely described as an endomorphism of the subobject representor, and Tierney showed that the conditions it needs to satisfy are just idempotence and the preservation of finite intersections. These "topologies" are important in both algebraic geometry and model theory because they determine the subtoposes as sheaf-categories.

Dalhousie University in 1969 set up a group of 15 Killam-supported researchers with Lawvere at the head; but in 1971 it terminated the group. Lawvere was controversial for his political opinions, for example, his opposition to the 1970 use of the War Measures Act, and for teaching the history of mathematics without permission.[2] But in 1995 Dalhousie hosted the celebration of 50 years of category theory with Lawvere and Saunders Mac Lane present.

Lawvere ran a seminar in Perugia, Italy (1972–1974) and especially worked on various kinds of enriched category. For example, a metric space can be regarded as an enriched category. From 1974 until his retirement in 2000 he was professor of mathematics at

professor emeritus of mathematics and adjunct professor emeritus of philosophy at Buffalo.[1]

Awards and honors

Selected books

See also

References

  1. ^ a b c Anderson, Dale (February 14, 2023), "Dr. F. William Lawvere, 85, UB professor who transformed advanced mathematics", The Buffalo News
  2. ^ Waite, P. (1997). "Lives of Dalhousie University: 1925-1980, The Old College Transformed", McGill-Queen's Press, pp 317-319
  3. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-27.

External links