Weakly Mal’tsev Categories and Strong Relations

Janelidze, Zurab; Martins-Ferreira, Nelson

Publication

Weakly Mal’tsev Categories and Strong Relations

2012Journal article

dc.contributor.author	Janelidze, Zurab
dc.contributor.author	Martins-Ferreira, Nelson
dc.date.accessioned	2025-10-29T13:53:21Z
dc.date.available	2025-10-29T13:53:21Z
dc.date.issued	2012
dc.description.abstract	We define a strong relation in a category C to be a span which is “orthogonal” to the class of jointly epimorphic pairs of morphisms. Under the presence of finite limits, a strong relation is simply a strong monomorphism R → X × Y . We show that a category C with pullbacks and equalizers is a weakly Mal’tsev category if and only if every reflexive strong relation in C is an equivalence relation. In fact, we obtain a more general result which includes, as its another particular instance, a similar well-known characterization of Mal’tsev categories.	eng
dc.description.sponsorship	The first author acknowledges the support of South African National Research Foundation and Georgian National Science Foundation (GNSF/ST09 730 3-105). The second author’s research was partially supported by FCT grant SFRH/BPD/43216/2008; also by ESTG and CDRSP from the Polytechnical Institute of Leiria.
dc.identifier.citation	Janelidze, Z., & Martins-Ferreira, N. (2012). Weakly Mal’tsev categories and strong relations. Theory and Applications of Categories, 27(5), 65-79.
dc.identifier.issn	1201-561X
dc.identifier.uri	http://hdl.handle.net/10400.8/14424
dc.language.iso	eng
dc.peerreviewed	yes
dc.relation	DESCENT OF INTERNAL CATEGORIES RELATIVE TO SPLIT EPIS
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject	Difunctional relation
dc.subject	Factorization system
dc.subject	Mal'tsev category
dc.subject	Weakly Mal'tsev category
dc.title	Weakly Mal’tsev Categories and Strong Relations	eng
dc.type	journal article
dspace.entity.type	Publication
oaire.awardTitle	DESCENT OF INTERNAL CATEGORIES RELATIVE TO SPLIT EPIS
oaire.awardURI	http://hdl.handle.net/10400.8/13633
oaire.citation.endPage	79
oaire.citation.issue	5
oaire.citation.startPage	65
oaire.citation.title	Theory and Applications of Categories
oaire.citation.volume	27
oaire.fundingStream	FARH
oaire.version	http://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyName	Martins-Ferreira
person.givenName	Nelson
person.identifier	485301
person.identifier.ciencia-id	B115-B65E-24AA
person.identifier.orcid	0000-0002-4199-7367
person.identifier.rid	N-1699-2013
person.identifier.scopus-author-id	24598020700
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