Sheaves on sites as Cauchy-complete categories

Derived Categories Of Sheaves

4 Derived Tensor 15 4.1 Tensor Product of Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Hoflat Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Derived Tensor Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Change of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Stacks and Sheaves of Categories as Fibrant Objects, Ii

We revisit what we call the fibred topology on a fibred category over a site and we prove a few basic results concerning this topology. We give a general result concerning the invariance of a 2-category of stacks under change of base.

Stacks and Sheaves of Categories as Fibrant Objects, I

We show that the category of categories fibred over a site is a generalized Quillen model category in which the weak equivalences are the local equivalences and the fibrant objects are the stacks, as they were defined by J. Giraud. The generalized model category restricts to one on the full subcategory whose objects are the categories fibred in groupoids. We show that the category of sheaves of...

Sites and Sheaves

Sites and Sheaves