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space. A category together with a choice of Grothendieck topology is called a site. Grothendieck topologies axiomatize the notion of an open cover. Using...

lattice of open sets as the basic notion of the theory, while Grothendieck topologies are structures defined on arbitrary categories that allow the definition...

many different Grothendieck topologies, each of which is well-suited for a different purpose. This is a list of some of the topologies on the category...

introduced Grothendieck topologies having in mind more exotic but geometrically finer and more sensitive examples than the crude Zariski topology, namely...

Alexander Grothendieck (/ˈɡroʊtəndiːk/; German pronunciation: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014) was...

constructible sheaves. Grothendieck originally introduced the machinery of Grothendieck topologies and topoi to define the étale topology. In this language...

fppf sheaves, but not as a sequence of etale sheaves. Using other Grothendieck topologies on ( F / S ) {\displaystyle (F/S)} gives alternative theories of...

connection Grothendieck construction Grothendieck duality Grothendieck existence theorem Grothendieck fibration Grothendieck's Galois theory Grothendieck group...

The Zariski topology in the set theoretic sense is then replaced by a Grothendieck topology. Grothendieck introduced Grothendieck topologies having in mind...

Alexandre Grothendieck solved this problem by introducing Grothendieck topologies, which axiomatize the notion of covering. Grothendieck's insight was...

Zariski topology in many Grothendieck topologies a torsor can be itself a covering. This happens in some of the most common Grothendieck topologies, such...

a Grothendieck topology. Thus a stack is formally given as a fibred category over another base category, where the base has a Grothendieck topology and...

theorem Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological...

<a_{n-1}<b_{1}<a_{n}} ), considering topologies (the standard topology in Euclidean space being a refinement of the trivial topology). When subdividing simplicial...

In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also plays...

{f^{-1}(s)}}\equiv f^{-1}({\bar {s}})} . Grothendieck topologies on a small category C are essentially the same as Lawvere–Tierney topologies on the topos of presheaves...

acquired an extended meaning, since it involved a Grothendieck topology. The idea of a Grothendieck topology (also known as a site) has been characterised...

In mathematics, a Grothendieck universe is a set U with the following properties: If x is an element of U and if y is an element of x, then y is also an...

several good properties possessed by its related "sub"topologies, such as the qfh and cdh topologies. It has subsequently been used by Beilinson to study...

Artin, Michael (1962), Grothendieck topologies, Harvard University, Dept. of Mathematics Artin, Michael (1972), Alexandre Grothendieck; Jean-Louis Verdier...