A categorical guide to separation, compactness and perfectness
type: Item
instance of: scholarly article
title: A categorical guide to separation, compactness and perfectness
zbMATH Open document ID: 0924.18003
published in: Homology, Homotopy and Applications
publication date: 1999-07-27T00:00:00Z
full work available at URL: https://eudml.org/doc/223622
full work available at URL: volume1-1.htm
review text: From the early seventies, there has been quite a number of publications, in particular by the present author, on categorical versions of the topological concepts in the title. Various levels of generality were considered, in particular in the choice of the class of morphisms (the ``closed'' maps) from which these concepts are defined. By developing the theory of separation and compactness from very general classes of morphisms, the author can compare several existing treatments of related concepts, making the paper, in particular, a useful guide indeed. In addition, the generalization allows applications to non-topological contexts, like extensive categories, Diers' algebraic sets and Janelidze's general Galois theory. (Here are a few light (but potentially annoying) mistakes detected by this reviewer. P. 150, line -13: ``\(m\cdot f\)'' should be ``\(f\cdot m\)''; line -7: ``\(\leq n\)'' should be ``\(\leq c_Y(n)\)''. P. 152, line 12: ``\(1_X\)'' should be ``\(1_Y\)''. P. 156, line -2: ``\(p^*_Z(!_Z)\)'' should be ``\(!_Y^*(!_Z)\)'').
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 1317843
zbMATH Keywords: separated object
zbMATH Keywords: compact object
zbMATH Keywords: embeddable object
zbMATH Keywords: absolute object
zbMATH Keywords: perfect morphisms
zbMATH Keywords: extensive categories
zbMATH Keywords: algebraic sets
zbMATH Keywords: general Galois theory
author: Walter Tholen
reviewed by: Michel Hébert
MaRDI profile type: Publication
DOI: 10.4310/HHA.1999.V1.N1.A6
description: scientific article; zbMATH DE number 1317843