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Session S27 - Categories and Topology

Thursday, July 15, 11:00 ~ 11:30 UTC-3

A cartesian closed category of algebraic theories

André Joyal

Université du Québec à Montréal (UQAM), Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

By an "algebraic theory" we mean a small category with finite products. A "combinatorial morphism" of algebraic theories $A\to B$ is defined to be a functor $Mod(A)\to Mod(B)$ preserving sifted colimits. For example, if $u:A\to B$ is a functor preserving products, then the pullback functor $u^\star:Mod(B)\to Mod(A)$ is a combinatorial morphism $B\to A$ and the pushforward functor $u_!:Mod(A)\to Mod(B)$ is a combinatorial morphism $A\to B$. We show that the 2-category of algebraic theories and combinatorial morphisms is cartesian closed.

Joint work with Marcelo Fiore (University of Cambridge, England).

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