@UNPUBLISHED{publication1, title = "Conjugation semigroups and conjugation monoids with cancellation", author = "{GARR{\~{A}}O, Ana Paula} and {MARTINS-FERREIRA, Nelson} and {RAPOSO, Margarida} and {SOBRAL, Manuela}", year = "2018-11-18", abstract = " We show that the category of conjugation semigroups with cancellation is weakly Mal'tsev and give a characterization of all admissible diagrams there. In the subcategory of conjugation monoids with cancellation 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 there. In this subcategory 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. ", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }