Strictification tensor product of 2-categories

Branko Nikolic

Strictification tensor product of 2-categories

Branko Nikolic^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

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 ☒D satisfying Lax(C, LaxpD, E)) ≅ [C ☒D, E] _lnt, hence generalising the case of the free distributive law 1 ☒ 1. We also discuss dual constructions.

Original language	English
Pages (from-to)	635-661
Number of pages	27
Journal	Theory and Application of Categories
Volume	34
Issue number	22
Publication status	Published - 2019

Keywords

Lax functor
strictification
distributive law
lax Gray product
free monoid

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T1 - Strictification tensor product of 2-categories

AU - Nikolic, Branko

PY - 2019

Y1 - 2019

N2 - 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 ☒D satisfying Lax(C, LaxpD, E)) ≅ [C ☒D, E] lnt, hence generalising the case of the free distributive law 1 ☒ 1. We also discuss dual constructions.

AB - 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 ☒D satisfying Lax(C, LaxpD, E)) ≅ [C ☒D, E] lnt, hence generalising the case of the free distributive law 1 ☒ 1. We also discuss dual constructions.

KW - Lax functor

KW - strictification

KW - distributive law

KW - lax Gray product

KW - free monoid

UR - https://www.scopus.com/pages/publications/85075220649

M3 - Article

SN - 1201-561X

VL - 34

SP - 635

EP - 661

JO - Theory and Application of Categories

JF - Theory and Application of Categories

IS - 22

ER -

Strictification tensor product of 2-categories

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Keywords

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