Partition complexes and trees

Gijs Heuts; Ieke Moerdijk

doi:10.1090/proc/16300

Partition complexes and trees

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Abstract

We construct a functor from the partition complex of a finite set A to a category of trees with leaves labelled by A and prove that it is homotopy initial. This construction and our proof are elementary and require very few preliminaries, but imply an equivalence between different bar constructions of an operad in great generality.

Original language	English
Pages (from-to)	2723-2732
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	6
Early online date	14 May 2023
DOIs	https://doi.org/10.1090/proc/16300
Publication status	Published - 1 Jun 2023

Bibliographical note

Publisher Copyright:
© 2023 American Mathematical Society.

Funding

Received by the editors December 16, 2021, and, in revised form, January 19, 2022, September 30, 2022, and October 5, 2022. 2020 Mathematics Subject Classification. Primary 55P48, 18M70. The first author was supported by the ERC through the grant ‘Chromatic homotopy theory of spaces’, nr. 950048.

Funders	Funder number
ERC	950048
European Research Council (ERC)	950048

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Partition complexes and treesFinal published version, 163 KBLicence: Taverne

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Partition complexes and trees

Abstract

Bibliographical note

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