Geodesic
Action representability via spans and prefibrations
Theory and applications of categories, Tome 32 (2017), pp. 1501-1521

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We give several reformulations of action representability of a category as well as action representability of its category of morphisms. In particular we show that for a semi-abelian category C, its category of morphisms is action representable if and only if the functor from the category of split extensions in C to C, sending a split extension to its kernel, is a prefibration. To obtain these reformulations we show that certain conditions are equivalent for right regular spans of categories.

Publié le :
Classification : 18A05, 18A22, 18A25, 18A40, 18A99, 18B99, 18D99
Keywords: action representable, semi-abelian, split extension, normalizer, prefibration, regular span 
@article{TAC_2017_32_a42,
     author = {J. R. A. Gray},
     title = {Action representability via spans and prefibrations},
     journal = {Theory and applications of categories},
     pages = {1501--1521},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a42/}
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J. R. A. Gray. Action representability via spans and prefibrations. Theory and applications of categories, Tome 32 (2017), pp. 1501-1521. http://geodesic.mathdoc.fr/item/TAC_2017_32_a42/