On weak higher dimensional categories. I: Part 1
type: Item
instance of: scholarly article
title: On weak higher dimensional categories. I: Part 1
zbMATH Open document ID: 0971.18005
DOI: 10.1016/S0022-4049(99)00179-6
author: Claudio Hermida
author: Michael Makkai
author: John Power
published in: Journal of Pure and Applied Algebra
publication date: 2001-10-28T00:00:00Z
review text: This is the first part of a three-part paper introducing the concept of multitopic set, which is intended as a foundation for a construction of weak higher-dimensional categories. Multitopic sets are analogous to the opetopic sets of \textit{J. C. Baez} and \textit{J. Dolan} [``Higher-dimensional algebra. III: \(n\)-categories and the algebra of opetopes'', Adv. Math. 135, No. 2, 145-206 (1998; Zbl 0909.18006)], but they are more geometric. A multitopic set consists of cells and pasting diagrams in various dimensions, where the pasting diagrams are got from the cells by amalgamation, using ideas from multicategory theory. Cells and pasting diagrams of dimension \(k\) have domains and codomains of dimension \(k-1\); the domains are arbitrary pasting diagrams but the codomains are cells. This first part of the paper consists of an informal introduction; details will be given in later parts.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 18A99
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 1538807
zbMATH Keywords: weak higher-dimensional category
zbMATH Keywords: multitopic set
zbMATH Keywords: pasting diagram
zbMATH Keywords: multicategory
zbMATH Keywords: opetopic sets
MaRDI profile type: Publication
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full work available at URL: s0022-4049(99)00179-6
OpenAlex ID: W2007590911
description: scientific article; zbMATH DE number 1538807