Hom weak ω-categories of a weak ω-category

Thomas Cottrell, Soichiro Fujii

Research output: Contribution to journalArticlepeer-review

Abstract

Classical definitions of weak higher-dimensional categories are given inductively, for example, a bicategory has a set of objects and hom categories, and a tricategory has a set of objects and hom bicategories. However, more recent definitions of weak n-categories for all natural numbers n, or of weak -categories, take more sophisticated approaches, and the nature of the 'hom is often not immediate from the definitions'. In this paper, we focus on Leinster's definition of weak -category based on an earlier definition by Batanin and construct, for each weak -category, an underlying (weak -category)-enriched graph consisting of the same objects and for each pair of objects x and y, a hom weak -category. We also show that our construction is functorial with respect to weak -functors introduced by Garner.

Original languageEnglish
Pages (from-to)420-441
Number of pages22
JournalMathematical Structures in Computer Science
Volume32
Issue number4
DOIs
Publication statusPublished - 12 Apr 2022

Data Availability Statement

No data were generated in association with this paper.

Funding

We gratefully acknowledge the support of Royal Society grant IE160402. The second author is supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST

Keywords

  • Weak ω-category
  • identity type
  • intensional Martin-Löf type theory
  • operad
  • weak ω-functor
  • weak ω-groupoid

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Hom weak ω-categories of a weak ω-category'. Together they form a unique fingerprint.

Cite this