Geodesic
Stability properties characterising n-permutable categories
Theory and applications of categories, Tome 32 (2017), pp. 1563-1587

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

The purpose of this paper is two-fold. A first and more concrete aim is to characterise n-permutable categories through certain stability properties of regular epimorphisms. These characterisations allow us to recover the ternary terms and the (n+1)-ary terms describing n-permutable varieties of universal algebras.

A second and more abstract aim is to explain two proof techniques, by using the above characterisation as an opportunity to provide explicit new examples of their use:
- an embedding theorem for n-permutable categories which allows us to follow the varietal proof to show that an n-permutable category has certain properties;
- the theory of unconditional exactness properties which allows us to remove the assumption of the existence of colimits, in particular when we use the approximate co-operations approach to show that a regular category is n-permutable.

Publié le :
Classification : 08A30, 08B05, 08C05, 18B15, 18B99, 18C99, 18A32
Keywords: Mal'tsev category, Goursat category, n-permutable category, embedding theorem, unconditional exactness property 
@article{TAC_2017_32_a44,
     author = {Pierre-Alain Jacqmin and Diana Rodelo},
     title = {Stability properties characterising n-permutable categories},
     journal = {Theory and applications of categories},
     pages = {1563--1587},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a44/}
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Pierre-Alain Jacqmin; Diana Rodelo. Stability properties characterising n-permutable categories. Theory and applications of categories, Tome 32 (2017), pp. 1563-1587. http://geodesic.mathdoc.fr/item/TAC_2017_32_a44/