Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/89458
Title: Cancellative conjugation semigroups and monoids
Authors: Garrão, Ana Paula
Martins-Ferreira, Nelson
Raposo, Margarida
Sobral, Manuela
Keywords: Admissibility diagrams; Weakly Mal’tsev category; Conjugation semigroups; Internal monoid; Internal groupoid
Issue Date: 2020
Publisher: Springer Verlag
Project: CMUC-UID/MAT/00324/2019 
Serial title, monograph or event: Semigroup Forum
Volume: 100
Abstract: We show that the category of cancellative conjugation semigroups is weakly Mal’tsev and give a characterization of all admissible diagrams there. In the category of cancellative conjugation monoids we describe, for Schreier split epimorphisms with codomain B and kernel X, all morphisms h:X→B which induce a reflexive graph, an internal category or an internal groupoid. We describe Schreier split epimorphisms in terms of external actions and consider the notions of precrossed semimodule, crossed semimodule and crossed module in the context of cancellative conjugation monoids. In this category we prove that a relative version of the so-called “Smith is Huq” condition for Schreier split epimorphisms holds as well as other relative conditions.
URI: http://hdl.handle.net/10316/89458
DOI: 10.1007/s00233-019-10070-9
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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