Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 881-917 |
| Number of pages | 37 |
| Journal | Journal of Homotopy and Related Structures |
| Volume | 14 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Dec 2019 |
Bibliographical note
Funding 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.
Funding 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.
Publisher Copyright:
© 2019, The Author(s).
Keywords
- Comonad cohomology
- Simplicial category
- Track category
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology