Geodesic
Monadic approach to Galois descent and cohomology
Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 92-112

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

We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg-Moore category of algebras over a suitable monad. This also suggests using monads directly, and our monadic approach to Galois descent makes no reference to Grothendieck descent theory at all. In order to make Galois descent constructions perfectly clear, we also describe their connections with some other related constructions of categorical algebra, and make various explicit calculations, especially with 1-cocycles and 1-dimensional non-abelian cohomology, usually omitted in the literature.

Classification : 18C15, 18D10
Keywords: Descent theory, Galois theory, monadic functor, group cohomology 
@article{TAC_2010_23_a4,
     author = {Francis Borceux and Stefaan Caenepeel and George Janelidze},
     title = {Monadic approach to {Galois} descent and cohomology},
     journal = {Theory and applications of categories},
     pages = {92--112},
     publisher = {mathdoc},
     volume = {23},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_23_a4/}
}
TY  - JOUR
AU  - Francis Borceux
AU  - Stefaan Caenepeel
AU  - George Janelidze
TI  - Monadic approach to Galois descent and cohomology
JO  - Theory and applications of categories
PY  - 2010
SP  - 92
EP  - 112
VL  - 23
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2010_23_a4/
LA  - en
ID  - TAC_2010_23_a4
ER  - 
%0 Journal Article
%A Francis Borceux
%A Stefaan Caenepeel
%A George Janelidze
%T Monadic approach to Galois descent and cohomology
%J Theory and applications of categories
%D 2010
%P 92-112
%V 23
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2010_23_a4/
%G en
%F TAC_2010_23_a4
Francis Borceux; Stefaan Caenepeel; George Janelidze. Monadic approach to Galois descent and cohomology. Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 92-112. http://geodesic.mathdoc.fr/item/TAC_2010_23_a4/