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 
@article{TAC_2008_21_a5,
     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/}
}
TY  - JOUR
AU  - N. Martins-Ferreira
TI  - Weakly Mal'cev categories
JO  - Theory and applications of categories
PY  - 2008
SP  - 91
EP  - 117
VL  - 21
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2008_21_a5/
LA  - en
ID  - TAC_2008_21_a5
ER  - 
%0 Journal Article
%A N. Martins-Ferreira
%T Weakly Mal'cev categories
%J Theory and applications of categories
%D 2008
%P 91-117
%V 21
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2008_21_a5/
%G en
%F TAC_2008_21_a5
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/