Comonad Cohomology of Track Categories

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 $2$-groupoid.

The paper has been re-written more concisely to improve readability. To appear in Journal of Homotopy and Related Structures