## View abstract

### 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. document.getElementById('cloak421f18fda6a6e68ae3ac99554b167d49').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy421f18fda6a6e68ae3ac99554b167d49 = 'j&#111;y&#97;l.&#97;ndr&#101;' + '&#64;'; addy421f18fda6a6e68ae3ac99554b167d49 = addy421f18fda6a6e68ae3ac99554b167d49 + '&#117;q&#97;m' + '&#46;' + 'c&#97;'; var addy_text421f18fda6a6e68ae3ac99554b167d49 = 'j&#111;y&#97;l.&#97;ndr&#101;' + '&#64;' + '&#117;q&#97;m' + '&#46;' + 'c&#97;';document.getElementById('cloak421f18fda6a6e68ae3ac99554b167d49').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy421f18fda6a6e68ae3ac99554b167d49 + '\'>'+addy_text421f18fda6a6e68ae3ac99554b167d49+'<\/a>';

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).