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Functorial Semantics of Algebraic Theories

This page is about William Lawvere‘s Ph.D. thesis:

  • F. W. Lawvere, Functorial Semantics of Algebraic Theories, Ph.D. thesis, Columbia University, 1963.

Written under S. Eilenberg and highly influential, the dissertation was not published at the time, and only two short notices appeared:

  • F. W. Lawvere, Functorial Semantics of Algebraic Theories, Proc. Nat. Acad. Sci. 50 (1963) pp. 869–872. (pdf)

  • F. W. Lawvere, Algebraic theories, algebraic categories, and algebraic functors, pp. 413–418 in Addison, Henkin, Tarski (eds.), The Theory of Models, North-Holland Amsterdam 1965.

It was finally published together with an author’s comment and a supplement here:

  • Reprints in Theory and Applications of Categories, No. 5 (2004) pp. 1–121 (tac).

In his thesis, Lawvere introduces Lawvere theories and the functorial perspective into model theory. He takes steps towards axiomatizing the category of categories as a foundation for mathematics. This includes introducing the notion of comma category as an auxiliary to a definition of adjunction implicitly involving an isomorphism of 2-sided discrete fibrations (cf. Lawvere 2004 pp.12–13).

For a generalization to relational theories see

category: reference

Last revised on August 16, 2020 at 01:15:03. See the history of this page for a list of all contributions to it.