A Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space.

19 апр. 2024 г. · A Grothendieck topology on a category is a choice of morphisms in that category which are regarded as covers.

A Grothendieck topology on C is a specification of a collection of families of maps {fi : Ui → X}i∈I, which we refer to as coverings, satisfying the following.

Let T be a topology and C a category with products. A presheaf on T with values in C is a functor F : T° — C. A sheaf F is a presheaf satisfying.

The naive fpqc topology is a Grothendieck topology defined by taking fpqc morphisms without the finiteness conditions, but it is not subcanonical. 1.6 ...

30 июл. 2012 г. · A Grothendieck topology by definition consists of sieves – what Johnstone calls a sifted coverage – whereas a Grothendieck pretopology in any ... Classical point-set topology using Grothendieck topologies Cohomology of Grothendieck topology - MathOverflow Why do Grothendieck topologies used in algebraic geometry ... Grothendieck topology for a non-small category - MathOverflow Другие результаты с сайта mathoverflow.net

2 окт. 2008 г. · Let T be a Grothendieck topology on a category C. A sieve. S ⊆ hU on an object U of C is said to belong to T if there exists a covering U of ...

16 апр. 2023 г. · Definition. The canonical topology on a category C C is the Grothendieck topology on C C which is the largest subcanonical topology.

28 дек. 2004 г. · This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.