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京都大学数理解析研究所

照井一成

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Time:    11:00-12:00, 10 May, 2018

Place:    Rm 478, Research Building 2, Main Campus, Kyoto University

    京都大学 本部構内 総合研究2号館 4階478号室

    http://www.kyoto-u.ac.jp/en/access/yoshida/main.html (Building 34)

Speaker: 藤井宗一郎 Soichiro Fujii (U Tokyo)

Title: A unified framework for notions of algebraic theory

Abstract:

Universal algebra uniformly captures various algebraic structures, by

expressing them as equational theories or (abstract) clones. The

ubiquity of algebraic structures in mathematics has also given rise to

several variants of universal algebra, such as symmetric and

non-symmetric operads, clubs, and monads. In this talk, I will present

a unified framework for these cousins of universal algebra, or notions

of algebraic theory.

First I will explain how each notion of algebraic theory can be

identified with a certain monoidal category, in such a way that

theories correspond to monoids. Then I will introduce a categorical

structure underlying the definition of models of theories. In specific

examples, it often arises in the form of oplax action or enrichment.

Finally I will uniformly characterize categories of models for various

notions of algebraic theory, by a double-categorical universal

property in the pseudo-double category of profunctors.