$\infty$-operads via symmetric sequences
Algebraic Topology
2021-03-16 v3 Category Theory
Abstract
We construct a generalization of the Day convolution tensor product of presheaves that works for certain double -categories. Using this construction, we obtain an -categorical version of the well-known description of (one-object) operads as associative algebras in symmetric sequences; more generally, we show that (enriched) -operads with varying spaces of objects can be described as associative algebras in a double -category of symmetric collections.
Cite
@article{arxiv.1708.09632,
title = {$\infty$-operads via symmetric sequences},
author = {Rune Haugseng},
journal= {arXiv preprint arXiv:1708.09632},
year = {2021}
}
Comments
50 pages. v2: Substantially rewritten with an improved version of the Day convolution construction, which produces a double $\infty$-category, v3: Various corrections