The algebraic structure of the universal complicial sets

Steiner, R. (2012) The algebraic structure of the universal complicial sets. Journal of Pure and Applied Algebra, 216(8-9), pp. 1976-1993. (doi: 10.1016/j.jpaa.2012.02.036)

Abstract

The nerve of a strict omega-category is a simplicial set with additional structure, making it into a so-called complicial set, and strict omega-categories are in fact equivalent to complicial sets. The nerve functor is represented by a sequence of strict omega-categories, called orientals, which are associated to simplexes. In this paper, we give a detailed algebraic description of the morphisms between orientals. The aim is to describe complicial sets algebraically, by operators and equational axioms.

• Item Type: Articles
• Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Pure and Applied Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Pure and Applied Algebra 216(8-9):1976-1993. DOI: 10.1016/j.jpaa.2012.02.036
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steiner, Dr Richard
• Authors: Steiner, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Pure and Applied Algebra
• Publisher: Elsevier
• ISSN: 0022-4049
• Published Online: 17 March 2012
• Copyright Holders: Copyright © 2012 Elsevier
• First Published: First published in Journal of Pure and Applied Algebra 216(8-9):1976-1993
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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