TY - JOUR
T1 - The Gray tensor product for 2-quasi-categories
AU - Maehara, Yuki
N1 - Funding Information:
This paper is based on the author's PhD thesis. He would like to thank his principle supervisor Dominic Verity for constant and helpful feedback throughout the project. He also gratefully acknowledges the support of an International Macquarie University Research Training Program Scholarship (Allocation Number: 2017127 ).
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/1/22
Y1 - 2021/1/22
N2 - 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.
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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U2 - 10.1016/j.aim.2020.107461
DO - 10.1016/j.aim.2020.107461
M3 - Article
AN - SCOPUS:85094562364
SN - 0001-8708
VL - 377
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 107461
ER -