Coalgebras in a category of classes
type: Item
instance of: scholarly article
title: Coalgebras in a category of classes
zbMATH Open document ID: 1112.18002
author: Michael A. Warren
published in: Annals of Pure and Applied Logic
publication date: 2007-04-18T00:00:00Z
review text: The author extends the familiar result that if \(C\) is a topos and \(G\) is a cartesian comonad of \(C,\) then the category of coalgebras \(C_{G} \) is also a topos in the setting of algebraic set theory [\textit{A. Joyal} and \textit{I. Moerdijk}, ``Algebraic set theory'', Lond. Math. Soc. Lect. Note Series 220 (1995; Zbl 0847.03025)]. In particular, it is shown that, under suitable assumptions, several kinds of categories of classes are stable under the formation of coalgebras for cartesian comonad, internal presheaves and comma categories.
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 03E70
zbMATH DE Number: 5144416
zbMATH Keywords: algebraic set theory
zbMATH Keywords: Cartesian comonad
zbMATH Keywords: coalgebra
zbMATH Keywords: internal presheaves
zbMATH Keywords: gluing
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: j.apal.2006.12.003
OpenAlex ID: W1977076690
cites work: Relating first-order set theories, toposes and categories of classes
cites work: Q4680361
cites work: Aspects of topoi
cites work: Q5718563
cites work: Q4853985
cites work: Sheaves in geometry and logic: a first introduction to topos theory
cites work: Type theories, toposes and constructive set theory: Predicative aspects of AST
DOI: 10.1016/J.APAL.2006.12.003
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description: scientific article; zbMATH DE number 5144416