## Presheaves of polynomial monads and Thomason's theorem

### Michael Batanin – 22 August 2018

In our joint paper with Florian De Leger we developed a version of Grothendieck's construction for Cat-algebras of polynomial monads. In this talk I explain that there is yet another version of Grothendieck's construction for polynomial monads this time we start from a presheaf of polynomial monads. In classical case (presheaf of small categories) these two constructions are isomorphic but in general they are quite different. I will prove then a version of Thomason's theorem on homotopy colimits related to the second construction (there is also a version of Thomason's theorem related to the first construction which I mentioned in one of my previous talks).

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