Partition complexes and trees
Algebraic Topology
2021-12-16 v1
Abstract
We construct a homotopy initial functor from the partition complex of a finite set to a category of trees with leaves labelled by . 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.
Cite
@article{arxiv.2112.08043,
title = {Partition complexes and trees},
author = {Gijs Heuts and Ieke Moerdijk},
journal= {arXiv preprint arXiv:2112.08043},
year = {2021}
}