Descent in categories of (co)algebras
type: Item
instance of: scholarly article
title: Descent in categories of (co)algebras
zbMATH Open document ID: 1081.18001
author: Bachuki Mesablishvili
published in: Homology, Homotopy and Applications
publication date: 2005-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/52076
full work available at URL: volume7-1.htm
review text: A morphism \(p: A'\to A\) of a category \({\mathcal A}\) is called an effective descent morphism whenever the pullback functor \(p^*: {\mathcal A}/A\to{\mathcal A}/A'\) is monadic. For an given endofunctor \(\Gamma: {\mathcal X}\to{\mathcal X}\) of a category \({\mathcal X}\), a \(\Gamma\)-algebra (resp. \(\Gamma\)-coalgebra) is a pair \((X,\alpha)\) of an object \(X\) of \({\mathcal X}\) and a morphism \(\alpha: \Gamma(X)\to X\) (resp. \(\alpha: X\to \Gamma(X)\)). With their natural morphisms, they constitute the category \({\mathcal X}^\Gamma\) (resp. \({\mathcal X}_\Gamma\)) of \(\Gamma\)-algebras (resp. \(\Gamma\)-coalgebras). In this paper, conditions are given under which a morphism of \(\Gamma\)-algebras (resp. \(\Gamma\)-coalgebras) is effective for descent.
reviewed by: Yves Diers
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 18C15
zbMATH DE Number: 2153123
zbMATH Keywords: effective descent
zbMATH Keywords: algebra
zbMATH Keywords: coalgebra
MaRDI profile type: Publication
DOI: 10.4310/HHA.2005.V7.N1.A1
description: scientific article; zbMATH DE number 2153123