internalization and categorical algebra
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This page is about:
Functorial Semantics of Algebraic Theories
Ph.D. thesis
Columbia University (1963)
(advised by Samuel Eilenberg)
which became highly influential in categorical algebra, see functorial semantics.
The dissertation was not published at the time, and only two short notices appeared:
F. William Lawvere: Functorial Semantics of Algebraic Theories, Proc. Nat. Acad. Sci. 50 (1963) 869-872 [doi:10.1073/pnas.50.5.869, pdf]
F. William Lawvere, Algebraic theories, algebraic categories, and algebraic functors, in: Addison, Henkin, Tarski (eds.), The Theory of Models, North-Holland Amsterdam (1965) 413-418 [doi:10.1016/B978-0-7204-2233-7.50044-7]
It was finally published together with an author’s comment and a supplement here:
In his thesis, Lawvere introduces what came to be called Lawvere theories and the functorial perspective into model theory. He also 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).
Generalization to relational theories:
Filippo Bonchi, Dusko Pavlovic, Pawel Sobocinski, Functorial Semantics for Relational Theories, [arXiv:1711.08699]
Chad Nester: A Variety Theorem for Relational Universal Algebra, Lecture Notes in Computer Science 13027 (2021) 362-377 [arXiv:2105.04958, doi:10.1007/978-3-030-88701-8_22]
Chad Nester: Partial And Relational Algebraic Theories, PhD thesis, Tallin University (2024) [doi:10.23658/taltech.4/2024]
Generalization to partial algebraic theories:
Last revised on February 18, 2025 at 15:24:31. See the history of this page for a list of all contributions to it.