A colimit decomposition for homotopy algebras in cat

John Bourke*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosický observed a key point to be that each homotopy colimit in SSet admits a decomposition into a homotopy sifted colimit of finite coproducts, and asked the author whether a similar decomposition holds in the 2-category of categories Cat. Our purpose in the present paper is to show that this is the case.

Original languageEnglish
Pages (from-to)13-28
Number of pages16
JournalApplied Categorical Structures
Issue number1
Publication statusPublished - Feb 2014
Externally publishedYes


  • Codescent object
  • Flexibility
  • Homotopy algebra


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