Comonad cohomology of track categories

David Blanc, Simona Paoli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)881-917
Number of pages37
JournalJournal of Homotopy and Related Structures
Issue number4
Early online date14 May 2019
Publication statusPublished - 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.

Publisher Copyright:
© 2019, The Author(s).


  • Comonad cohomology
  • Simplicial category
  • Track category


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