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Dimitri Zaganidis "On a (∞,2)-category of homotopy coherent adjunctions in an ∞-cosmos.'"
Start Date: 4/16/2018Start Time: 4:30 PM
End Date: 4/16/2018End Time: 5:30 PM
Event Description:
Speaker: Dimitri Zaganidis, EPFL

Abstract: Riehl and Verity initiated a program to study the category theory of (∞,1)-categories in a model-independent way, through the study of ∞-cosmoi. Homotopy coherent monads in an ∞

-cosmos are of particular interest since they determine an Eilenberg-Moore object of (homotopy coherent) algebras.

In this talk, I will generalize the graphical calculus of Riehl and Verity to provide a combinatorial description of the simplicial categories Adjhc[n]
and Mndhc[n]. They encode homotopy coherent diagrams of homotopy coherent adjunctions and monads of the shape of the simplex Δ[n], and in particular for n=1

, provide appropriate definitions for homotopy coherent morphisms of adjunctions and monads.

I will briefly introduce weak complicial sets and show that the nerve induced by Adjhc[−]:Δ→sSet−Cat
gives rise to an (∞,2)-category of homotopy coherent adjunctions. If time permits, I will discuss a related conjecture for homotopy coherent monads.
Location Information:
Homewood - Krieger
Room: 302
Mathematics Department
Topology Seminar

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