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University of Cambridge > Talks.cam > Category Theory Seminar > Comonad cohomology of track categories

## Comonad cohomology of track categoriesAdd to your list(s) Download to your calendar using vCal - Simona Paoli (University of Leicester)
- Tuesday 06 March 2018, 14:15-15:15
- MR5, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Tamara von Glehn. Simplicial categories are one of the models of (∞,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. This talk is part of the Category Theory Seminar series. ## This talk is included in these lists:- All CMS events
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