The Gray tensor product for 2-quasi-categories

Yuki Maehara

doi:10.1016/j.aim.2020.107461

The Gray tensor product for 2-quasi-categories

Yuki Maehara

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We construct an (∞,2)-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an n-ary) functor on the category of Θ₂-sets, and it is shown to be left Quillen with respect to Ara's model structure. Moreover we prove that this tensor product forms part of a “homotopical” (biclosed) monoidal structure, or more precisely a normal lax monoidal structure that is associative up to homotopy.

Original language	English
Article number	107461
Pages (from-to)	1-78
Number of pages	78
Journal	Advances in Mathematics
Volume	377
Early online date	28 Oct 2020
DOIs	https://doi.org/10.1016/j.aim.2020.107461
Publication status	Published - 22 Jan 2021

Keywords

2-quasi-category
Gray tensor product

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10.1016/j.aim.2020.107461

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AB - We construct an (∞,2)-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an n-ary) functor on the category of Θ2-sets, and it is shown to be left Quillen with respect to Ara's model structure. Moreover we prove that this tensor product forms part of a “homotopical” (biclosed) monoidal structure, or more precisely a normal lax monoidal structure that is associative up to homotopy.

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The Gray tensor product for 2-quasi-categories

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Keywords

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