Geodesic
Weakly Mal'cev categories
Theory and applications of categories, The Tholen Festschrift, Tome 21 (2008), pp. 91-117

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We introduce a notion of weakly Mal'cev category, and show that: (a) every internal reflexive graph in a weakly Mal'tsev category admits at most one multiplicative graph structure in the sense of Janelidze, and such a structure always makes it an internal category; (b) (unlike the special case of Mal'tsev categories) there are weakly Mal'tsev categories in which not every internal category is an internal groupoid. We also give a simplified characterization of internal groupoids among internal categories in this context.

Classification : Primary 18E05, Secondary 18B40
Keywords: Admissible reflexive graph, multiplicative graph, internal category, internal groupoid, weakly Mal'cev category, naturally weakly Mal'cev category, Mal'cev variety of universal algebras 
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     author = {N. Martins-Ferreira},
     title = {Weakly {Mal'cev} categories},
     journal = {Theory and applications of categories},
     pages = {91--117},
     publisher = {mathdoc},
     volume = {21},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2008_21_a5/}
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N. Martins-Ferreira. Weakly Mal'cev categories. Theory and applications of categories, The Tholen Festschrift, Tome 21 (2008), pp. 91-117. http://geodesic.mathdoc.fr/item/TAC_2008_21_a5/