10 февр. 2018 г. · The whole point of Grothendieck topologies is to apply insights from topological reasoning in contexts (some within algebraic topology of a very modern flavor)

30 июл. 2012 г. · A Grothendieck topology by definition consists of sieves – what Johnstone calls a sifted coverage – whereas a Grothendieck pretopology in any ...

24 янв. 2013 г. · To define a Grothendieck topology of a category, we usually require that the category is small. Question 1: Why do we need to require the category to be small?

22 нояб. 2022 г. · Generally in one of these topologies, a cover of schemes is a family of maps which is jointly surjective on points, such that each map in the ...

6 мар. 2015 г. · The Grothendieck construction is the category F≀C with objects being pairs (c,x) where c is a object of C and x∈F(c).

26 июл. 2019 г. · Etale topology, required to define etale cohomology, is not a topology in the usual sense. It is Grothendieck topology only.

10 янв. 2023 г. · The Grothendieck topology on any category for which only the identity morphisms are covering is the trivial topology. Its sheaves are all the presheaves.

17 июн. 2021 г. · The focus is specifically on how to define cohomology in a topos, as opposed to many references on topos theory aimed more in the direction of algebraic stacks.

24 окт. 2010 г. · I am trying to think about certain problems in the theory of motives without having a proper background in Grothendieck topologies and the like.

26 окт. 2023 г. · Defining a Grothendieck topology on Prop amounts to defining a Grothendieck topology on Propλ for each λ≥0. In this way, in order to classify ...