From operator categories to higher operads
| Autor: | Clark Barwick |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Leinster category
010102 general mathematics Boardman–Vogt tensor product wreath product Mathematics::Algebraic Topology Segal spaces 01 natural sciences $\infty$–operads Algebra Operator (computer programming) 18D50 Wreath product Mathematics::Category Theory 0103 physical sciences operator categories $E_n$–operads 55U40 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Geom. Topol. 22, no. 4 (2018), 1893-1959 Barwick, C 2018, ' From operator categories to higher operads ', Geometry and Topology, vol. 22, no. 4, pp. 1893-1959 . https://doi.org/10.2140/gt.2018.22.1893 |
| ISSN: | 1364-0380 1465-3060 |
| DOI: | 10.2140/gt.2018.22.1893 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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