From operator categories to higher operads

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Abstract

In this paper we introduce the notion of an operator category and two different models for homotopy theory of ∞-operads over an operator category - one of which extends Lurie's theory of ∞-operads, the other of which is completely new, even in the commutative setting. We define perfect operator categories, and we describe a category Λ(Φ) attached to a perfect operator category Φ that provides Segal maps. We define a wreath product of operator categories and a form of the Boardman-Vogt tensor product that lies over it. We then give examples of operator categories that provide universal properties for the operads An and En (1≤ n ≤ +∞), as well as a collection of new examples.
Original languageEnglish
Pages (from-to)1893-1959
Number of pages50
JournalGeometry and Topology
Volume22
Issue number4
DOIs
Publication statusPublished - 5 Apr 2018

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