The Gray tensor product for 2-quasi-categories

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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 languageEnglish
Article number107461
JournalAdvances in Mathematics
Volume377
DOIs
Publication statusPublished - Jan 22 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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