Browsing by Author "Sobral, M."
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- Cancellative conjugation semigroups and monoidsPublication . Garrão, A. P.; Martins-Ferreira, Nelson; Raposo, M.; Sobral, M.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.
- Schreier split extensions of preordered monoidsPublication . Martins-Ferreira, N.; Sobral, M.Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories are related between them by appropriate functors as well as with the categories of preordered sets and of monoids. Schreier split extensions are described in the full subcategory of preordered monoids whose preorder is determined by the corresponding positive cone.