Explore: Grothendieck Categories

Alexander Grothendieck, later Alexandre Grothendieck in French (/ˈɡroʊtəndiːk/; German: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 –

study of (certain) Grothendieck categories. By definition, a Grothendieck category A {\displaystyle {\mathcal {A}}} is an AB5 category with a generator

extensions of the theorem exist. One concerns Grothendieck categories: if G is a Grothendieck category with an Artinian generator, then every Artinian

algebraic geometry, cohomology and pure category theory. Mac Lane says Alexander Grothendieck defined abelian categories in 1957, but there is a reference that

In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets

Dolbeault-Grothendieck lemma Grothendieck's axioms Grothendieck category Grothendieck's comparison theorem Grothendieck's connectedness theorem Grothendieck connection

Grothendieck universe.) However, one does not work directly with the "category of all sets". Instead, theorems are expressed in terms of the category

The approach of Alexander Grothendieck is concerned with the category-theoretic properties that characterise the categories of finite G-sets for a fixed

homomorphic image of the Grothendieck group of M. The Grothendieck group construction takes its name from a specific case in category theory, introduced by

like the category of sets and possess a notion of localization. The Grothendieck topoi find applications in algebraic geometry, and more general elementary