Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43870
Title: The Cuboid Lemma and Mal’tsev Categories
Authors: Gran, Marino 
Rodelo, Diana 
Issue Date: 2013
Publisher: Springer
Project: info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT 
Serial title, monograph or event: Applied Categorical Structures
Volume: 22
Issue: 5-6
Abstract: We prove that a regular category ℂ is a Mal’tsev category if and only if a strong form of the denormalised 3 × 3 Lemma holds true in ℂ. In this version of the 3 × 3 Lemma, the vertical exact forks are replaced by pullbacks of regular epimorphisms along arbitrary morphisms. The shape of the diagram it determines suggests to call it the Cuboid Lemma. This new characterisation of regular categories that are Mal’tsev categories (= 2-permutable) is similar to the one previously obtained for Goursat categories (= 3-permutable). We also analyse the “relative” version of the Cuboid Lemma and extend our results to that context.
URI: http://hdl.handle.net/10316/43870
Other Identifiers: 10.1007/s10485-013-9352-5
DOI: 10.1007/s10485-013-9352-5
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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