From operator categories to higher operads

Barwick, Clark¹

¹ School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom

Geometry & topology, Tome 22 (2018) no. 4, pp. 1893-1959.

Résumé

We introduce the notion of an operator category and two different models for homotopy theory of $\infty$–operads over an operator category — one of which extends Lurie’s theory of $\infty$–operads, the other of which is completely new, even in the commutative setting. We define perfect operator categories, and we describe a category $\Lambda \left(\Phi \right)$ attached to a perfect operator category $\Phi$ 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 $A_n$ and $E_n$ ($1\le n\le +\infty$) and also a collection of new examples.

Détail

DOI : 10.2140/gt.2018.22.1893

Classification : 18D50, 55U40
Keywords: operator categories, $\infty$–operads, $E_n$–operads, wreath product, Boardman–Vogt tensor product, Leinster category, Segal spaces

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