nLab
category of descent data

Idea

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Descent along a cover

This kind of descent is described in the article stack using the bar construction to write a sieve as a colimit of representables.

Let C be a site, p:DC a fibration, xC 0, U x a cover of x. h xC/x the full subcategory of arrows, that factor through some ux of the cover; the corresponding functor C opCat is then a sieve. The category of descent data (sometimes shortcut to descent category) of p along U x is defined to be the functor category [h x,D].

See also

descent

descent object

stack

References

  • Angelo Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory (arXiv) (p.74)
Revised on September 29, 2011 03:15:11 by Zoran Škoda (161.53.130.104)