(…)
This kind of descent is described in the article stack using the bar construction to write a sieve as a colimit of representables.
Let be a site, a fibration, , a cover of . the full subcategory of arrows, that factor through some of the cover; the corresponding functor is then a sieve. The category of descent data (sometimes shortcut to descent category) of along is defined to be the functor category .
Last revised on June 11, 2022 at 16:34:13. See the history of this page for a list of all contributions to it.