Geodesic
Finite categories with pushouts
Theory and applications of categories, Tome 30 (2015), pp. 1017-1031

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

Let C be a finite category. For an object X of C one has the hom-functor Hom(-,X) of C to Set. If G is a subgroup of Aut(X), one has the quotient functor Hom(-,X)/G. We show that any finite product of hom-functors of C is a sum of hom-functors if and only if C has pushouts and coequalizers and that any finite product of hom-functors of C is a sum of functors of the form \Hom(-,X)/G if and only if C has pushouts. These are variations of the fact that a finite category has products if and only if it has coproducts.

Publié le :
Classification : 18A30, 18A35
Keywords: pushout, coequalizer, hom-functor, familially representable functor, nearly representable functor 
@article{TAC_2015_30_a29,
     author = {D. Tambara},
     title = {Finite categories with pushouts},
     journal = {Theory and applications of categories},
     pages = {1017--1031},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a29/}
}
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D. Tambara. Finite categories with pushouts. Theory and applications of categories, Tome 30 (2015), pp. 1017-1031. http://geodesic.mathdoc.fr/item/TAC_2015_30_a29/