Comonad Cohomology of Track Categories
Algebraic Topology
2019-04-16 v3 Category Theory
Abstract
We define a comonad cohomology of track categories and we show it is linked by a long exact sequence to its Dwyer-Kan-Smith cohomology . Under mild hypothesis on the track category, we show that its comonad cohomology coincides, up to dimension shift, with its Dwyer-Kan-Smith cohomology, therefore obtaining an algebraic formulation of the latter. We also specialize our results to the case where the track category is a -groupoid.
Keywords
Cite
@article{arxiv.1801.05065,
title = {Comonad Cohomology of Track Categories},
author = {David Blanc and Simona Paoli},
journal= {arXiv preprint arXiv:1801.05065},
year = {2019}
}
Comments
The paper has been re-written more concisely to improve readability. To appear in Journal of Homotopy and Related Structures