Homomorphisms of higher categories

Richard Garner

doi:10.1016/j.aim.2010.01.022

Homomorphisms of higher categories

Richard Garner^*

^*Corresponding author for this work

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

18 Citations (Scopus)

Abstract

We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction is such that these homomorphisms admit a strictly associative and unital composition. We give two applications of this construction. The first is to tricategories; and here we do not obtain the trihomomorphisms defined by Gordon, Power and Street, but rather something which is equivalent in a suitable sense. The second application is to Batanin's weak ω-categories.

Original language	English
Pages (from-to)	2269-2311
Number of pages	43
Journal	Advances in Mathematics
Volume	224
Issue number	6
DOIs	https://doi.org/10.1016/j.aim.2010.01.022
Publication status	Published - Aug 2010
Externally published	Yes

Keywords

Abstract homotopy theory
Higher-dimensional categories
Weak morphisms

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10.1016/j.aim.2010.01.022

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AB - We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction is such that these homomorphisms admit a strictly associative and unital composition. We give two applications of this construction. The first is to tricategories; and here we do not obtain the trihomomorphisms defined by Gordon, Power and Street, but rather something which is equivalent in a suitable sense. The second application is to Batanin's weak ω-categories.

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KW - Weak morphisms

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Homomorphisms of higher categories

Abstract

Keywords

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