The Todd-Coxeter procedure and left Kan extensions
type: Item
instance of: scholarly article
title: The Todd-Coxeter procedure and left Kan extensions
zbMATH Open document ID: 0838.18002
author: S. Carmody
author: M. Leeming
author: R. F. C. Walters
published in: Journal of Symbolic Computation
publication date: 1996-05-27T00:00:00Z
review text: We introduce a generalization of the Todd-Coxeter procedure for the enumeration of cosets. The generalized procedure relates to a construction in category theory known as the left Kan extension. It admits a great variety of applications, including enumerating cosets, computing certain colimits in the category of \({\mathcal S}ets\), and enumerating the arrows in a category given by generators and relations. We begin by defining the notion of a left Kan extension, and giving a number of illustrative examples. We then provide a full specification of the procedure, followed by its application in relation to each of the examples. Finally, we provide a formulation of the procedure in terms of graphs and presentations of actions of graphs (automata) which is more convenient for theoretical purposes. [See also the second and third author, in: Computational algebra and number theory, Math. Appl., Dordr. 325, 53-73 (1995; Zbl 0827.18001)].
reviewed by: Nantel Bergeron
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18B20
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 18-04
Mathematics Subject Classification ID: 20B40
zbMATH DE Number: 826854
zbMATH Keywords: computational algebra
zbMATH Keywords: Todd-Coxeter procedure
zbMATH Keywords: enumeration of cosets
zbMATH Keywords: left Kan extension
zbMATH Keywords: generators
zbMATH Keywords: relations
MaRDI profile type: Publication
full work available at URL: jsco.1995.1027
OpenAlex ID: W2042767697
DOI: 10.1006/JSCO.1995.1027
description: scientific article; zbMATH DE number 826854