Geodesic
Descent in monoidal categories
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 210-221

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

We consider a symmetric monoidal closed category $V = (V, \otimes, I, [-,-])$ together with a regular injective object $Q$ such that the functor $[-, Q] : \to V^{op}$ is comonadic and prove that in such a category, as in the monoidal category of abelian groups, a morphism of commutative monoids is an effective descent morphism for modules if and only if it is a pure monomorphism. Examples of this kind of monoidal categories are elementary toposes considered as cartesian closed monoidal categories, the module categories over a commutative ring object in a Grothendieck topos and Barr's star-autonomous categories.

Publié le :
Classification : 18A20, 18D10, 18D35
Keywords: symmetric monoidal categories, effective descent morphisms, pure morphisms 
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     author = {Bachuki Mesablishvili},
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     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a9/}
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Bachuki Mesablishvili. Descent in monoidal categories. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 210-221. http://geodesic.mathdoc.fr/item/TAC_2012_27_a9/