Quasitoposes, quasiadhesive categories and Artin glueing

Peter T. Johnstone*, Stephen Lack, Pawel Sobociński

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

14 Citations (Scopus)

Abstract

Adhesive categories are a class of categories in which pushouts along monos are well-behaved with respect to pullbacks. Recently it has been shown that any topos is adhesive. Many examples of interest to computer scientists are not adhesive, a fact which motivated the introduction of quasiadhesive categories. We show that several of these examples arise via a glueing construction which yields quasitoposes. We show that, surprisingly, not all such quasitoposes are quasiadhesive and characterise precisely those which are by giving a succinct necessary and sufficient condition on the lattice of subobjects.

Original languageEnglish
Title of host publicationAlgebra and Coalgebra in Computer Science - Second International Conference, CALCO 2007, Proceedings
EditorsT. Mossakowski, U. Montanari, M. Haveraaen
Place of PublicationBerlin; Heidelberg
PublisherSpringer, Springer Nature
Pages312-326
Number of pages15
ISBN (Print)9783540738572
Publication statusPublished - 2007
Externally publishedYes
Event2nd International Conference on Algebra and Coalgebra in Computer Science, CALCO 2007 - Bergen, Norway
Duration: 20 Aug 200724 Aug 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4624
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Conference on Algebra and Coalgebra in Computer Science, CALCO 2007
CountryNorway
CityBergen
Period20/08/0724/08/07

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