# Next week, Wednesday at 11:00, U. Haifa Topology & Geometry seminar on September 11, 2019

Geometry & Topology Seminar

Speaker: Paoli Simona (University of Leicester)

Topic: Comonad cohomology of track categories

Place:    Room 614 in the Science & Education Building

Time:   11:00

Date:  Wednesday, September 11, 2019

Abstract:

Simplicial categories are one of the models of (\infty,1)-categories. They can be studied using the Postnikov decomposition, whose sections are categories enriched in simplicial n-types and whose k-invariants are defined in terms of the (S,O)-cohomology of Dwyer, Kan and Smith. The latter is defined topologically, while the understanding of the k-invariants calls for an algebraic description. In this talk I illustrate the first step of this program, for categories enriched in groupoids, also called track category. We define a comonad cohomology of track categories and we show that, under mild hypothesis on the track category, its comonad cohomology coincides up to a dimension shift, with its (S,O)-cohomology, therefore obtaining an algebraic formulation of the latter. This is joint work with David Blanc.

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