The intersection of algebra and coalgebra
type: Item
instance of: scholarly article
title: The intersection of algebra and coalgebra
zbMATH Open document ID: 1110.18002
author: Jiří Adámek
published in: Theoretical Computer Science
publication date: 2007-01-09T00:00:00Z
review text: The aim of this paper is to prove that if a category is a variety of \(F\)-algebras and as well as a covariety of \(G\)-algebras for endofunctors \(F\) and \(G\) of many-sorted sets, then it is a presheaf category (shortly, algebra \(\cap \) coalgebra = presheaves). The main result is that all coalgebras on a set functor \(H\) form a presheaf category iff \(H\) is a reduction of a polynomial functor. The present paper is an expanded version of \textit{J. Adámek} [Lect. Notes Comput. Sci. 3629, 67--82 (2005; Zbl 1151.18004)] presented at the conference on algebra and coalgebra in computer science, CALCO 2005, in Swansea.
reviewed by: Dana Piciu
Mathematics Subject Classification ID: 18C05
Mathematics Subject Classification ID: 18B20
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 68Q99
zbMATH DE Number: 5083520
zbMATH Keywords: variety
zbMATH Keywords: covariety
zbMATH Keywords: presheaf category
MaRDI profile type: Publication
full work available at URL: j.tcs.2006.07.004
OpenAlex ID: W1968654628
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DOI: 10.1016/J.TCS.2006.07.004
description: scientific article; zbMATH DE number 5083520