Partition complexes and trees

Published 15 Dec 2021 in math.AT | (2112.08043v1)

Abstract: We construct a homotopy initial functor from the partition complex of a finite set $A$ to a category of trees with leaves labelled by $A$. As an application, this provides an equivalence between different bar constructions of an operad. In the differential graded case, this gives a very elementary proof of an equivalence originally due to Fresse.

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