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 
@article{TAC_2012_27_a9,
     author = {Bachuki Mesablishvili},
     title = {Descent in monoidal categories},
     journal = {Theory and applications of categories},
     pages = {210--221},
     publisher = {mathdoc},
     volume = {27},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a9/}
}
TY  - JOUR
AU  - Bachuki Mesablishvili
TI  - Descent in monoidal categories
JO  - Theory and applications of categories
PY  - 2012
SP  - 210
EP  - 221
VL  - 27
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2012_27_a9/
LA  - en
ID  - TAC_2012_27_a9
ER  - 
%0 Journal Article
%A Bachuki Mesablishvili
%T Descent in monoidal categories
%J Theory and applications of categories
%D 2012
%P 210-221
%V 27
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2012_27_a9/
%G en
%F TAC_2012_27_a9
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/