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

14 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

Access to Document

10.1016/j.aim.2010.01.022

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Homomorphisms of higher categories'. Together they form a unique fingerprint.

Cite this

@article{3d194941a2134396891fe5cdc9e049a6,

title = "Homomorphisms of higher categories",

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.",

keywords = "Abstract homotopy theory, Higher-dimensional categories, Weak morphisms",

author = "Richard Garner",

year = "2010",

month = aug,

doi = "10.1016/j.aim.2010.01.022",

language = "English",

volume = "224",

pages = "2269--2311",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Elsevier",

number = "6",

}

TY - JOUR

T1 - Homomorphisms of higher categories

AU - Garner, Richard

PY - 2010/8

Y1 - 2010/8

N2 - 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.

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.

KW - Abstract homotopy theory

KW - Higher-dimensional categories

KW - Weak morphisms

UR - http://www.scopus.com/inward/record.url?scp=77953291468&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2010.01.022

DO - 10.1016/j.aim.2010.01.022

M3 - Article

AN - SCOPUS:77953291468

VL - 224

SP - 2269

EP - 2311

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 6

ER -