#
Strictification tensor product of 2-categories

##
Branko Nikolic

Given 2-categories C and D, let Lax (C,D) denote the 2-category of lax
functors, lax natural transformations and modifications, and [C,D]_lnt its
full sub-2-category of (strict) 2-functors. We give two isomorphic
constructions of a 2-category C \boxtimes D satisfying Lax (C, Lax(D,E))
\cong [C \boxtimes D, E}_lnt, hence generalising the case of the free
distributive law 1 \boxtimes 1. We also discuss dual constructions.

Keywords:
Lax functor, strictification, distributive law, lax Gray product, free
monoid

2010 MSC:
18D05, 18D35, 18G30

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 22, pp 635-661.

Published 2019-08-13.

http://www.tac.mta.ca/tac/volumes/34/22/34-22.pdf

TAC Home