Applied Categorical Structures

, Volume 22, Issue 1, pp 13–28 | Cite as

A Colimit Decomposition for Homotopy Algebras in Cat

  • John Bourke


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.


Homotopy algebra Flexibility Codescent object 

Mathematics Subject Classifications (2010)

18D05 55U35 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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