Distributivity of categories of coalgebras
type: Item
instance of: scholarly article
title: Distributivity of categories of coalgebras
zbMATH Open document ID: 1061.18003
DOI: 10.1016/S0304-3975(02)00582-0
author: H. Peter Gumm
author: Jesse Hughes
author: T. Schröder
published in: Theoretical Computer Science
publication date: 2004-10-27T00:00:00Z
review text: Categories of coalgebras for an endofunctor (of the category of sets, or of something fairly similar) play an important role in the semantics of computation. One conceptual difficulty in working with such categories is that, whilst the forgetful functor to the underlying category creates colimits, it does not in general create limits; in particular, products in such categories tend to be hard to describe. In this paper, the authors investigate when finite products distribute over finite coproducts in a category of coalgebras, and the closely related question of when such a category is extensive. Unsurprisingly, their results turn out to be similar to those obtained by the reviewer, \textit{J.~Power, T.~Tsujishita, H.~Watanabe} and \textit{J.~Worrell} [Theor. Comput. Sci. 260, 87--117 (2001; Zbl 0973.68178)] on the question of when such a category is a topos.
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 68Q85
zbMATH DE Number: 2110976
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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full work available at URL: s0304-3975(02)00582-0
OpenAlex ID: W1968036898
description: scientific article; zbMATH DE number 2110976