Localisations of locally presentable categories. II
type: Item
instance of: scholarly article
title: Localisations of locally presentable categories. II
zbMATH Open document ID: 0705.18006
DOI: 10.1016/0022-4049(90)90068-S
author: Elsie Sterbin Gottlieb
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: This is a continuation of Part I [ibid. 58, No.3, 227-233 (1989; Zbl 0677.18009)]. However, it does not deal with enriched categories; the authors content themselves to consider localizations E of categories \(A=Lex(C^{op},Set)\). They show how E arises as Lex Sh\({}_ J(C)\) for a Grothendieck topology on C. Moreover, they give twelve good structural aspects of C and show how they transfer to A. For instance, if C is an elementary topos, then A is a locally finitely presentable Grothendieck topos and the Yoneda embedding y: \(C\to A\) is a fully faithfull logical morphism.
Mathematics Subject Classification ID: 18E35
Mathematics Subject Classification ID: 18F10
zbMATH DE Number: 4156723
zbMATH Keywords: locally presentable categories
zbMATH Keywords: localization of categories
zbMATH Keywords: Grothendieck topology
zbMATH Keywords: elementary topos
zbMATH Keywords: Grothendieck topos
zbMATH Keywords: Yoneda embedding
Wikidata QID: Q56687262
reviewed by: Heinrich Kleisli
MaRDI profile type: Publication
cites work: Q5628320
cites work: Representation of categories
cites work: On locales of localizations
cites work: On closed categories of functors
cites work: A reflection theorem for closed categories
cites work: Localisation of locally presentable categories
cites work: Lokal präsentierbare Kategorien. (Locally presentable categories)
cites work: Cosmoi of Internal Categories
full work available at URL: 0022-4049(90)90068-s
OpenAlex ID: W2069453917
description: scientific article; zbMATH DE number 4156723