We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding (S,O)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the (S,O)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.
Bibliographical noteFunding Information:
We would like to thank the referee for his or her pertinent and helpful comments. The first author was supported by the Israel Science Foundation grants 74/11 and 770/16. The second author would like to thank the Department of Mathematics of the University of Haifa for its hospitality during several visits. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
© 2019, The Author(s).
- Comonad cohomology
- Simplicial category
- Track category