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- Tannakian_category abstract "In mathematics, a tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to approximate, in some sense, the category of linear representations of an algebraic group G defined over K. A number of major applications of the theory have been made, or might be made in pursuit of some of the central conjectures of contemporary algebraic geometry and number theory.The name is taken from Tannaka–Krein duality, a theory about compact groups G and their representation theory. The theory was developed first in the school of Alexander Grothendieck. It was later reconsidered by Pierre Deligne, and some simplifications made. The pattern of the theory is that of Grothendieck's Galois theory, which is a theory about finite permutation representations of groups G which are profinite groups.The gist of the theory, which is rather elaborate in detail in the exposition of Saavedra Rivano, is that the fiber functor Φ of the Galois theory is replaced by a tensor functor T from C to K-Vect. The group of natural transformations of Φ to itself, which turns out to be a profinite group in the Galois theory, is replaced by the group (a priori only a monoid) of natural transformations of T into itself, that respect the tensor structure. This is by nature not an algebraic group, but an inverse limit of algebraic groups (pro-algebraic group).".
- Tannakian_category wikiPageExternalLink tc.html.
- Tannakian_category wikiPageExternalLink tc.pdf.
- Tannakian_category wikiPageID "7221237".
- Tannakian_category wikiPageRevisionID "599893295".
- Tannakian_category hasPhotoCollection Tannakian_category.
- Tannakian_category subject Category:Algebraic_groups.
- Tannakian_category subject Category:Duality_theories.
- Tannakian_category subject Category:Monoidal_categories.
- Tannakian_category type Abstraction100002137.
- Tannakian_category type AlgebraicGroups.
- Tannakian_category type Class107997703.
- Tannakian_category type Cognition100023271.
- Tannakian_category type Collection107951464.
- Tannakian_category type DualityTheories.
- Tannakian_category type Explanation105793000.
- Tannakian_category type Group100031264.
- Tannakian_category type HigherCognitiveProcess105770664.
- Tannakian_category type MonoidalCategories.
- Tannakian_category type Process105701363.
- Tannakian_category type PsychologicalFeature100023100.
- Tannakian_category type Theory105989479.
- Tannakian_category type Thinking105770926.
- Tannakian_category comment "In mathematics, a tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to approximate, in some sense, the category of linear representations of an algebraic group G defined over K.".
- Tannakian_category label "Tannakian category".
- Tannakian_category label "淡中圏".
- Tannakian_category sameAs 淡中圏.
- Tannakian_category sameAs m.025wl26.
- Tannakian_category sameAs Q7683609.
- Tannakian_category sameAs Q7683609.
- Tannakian_category sameAs Tannakian_category.
- Tannakian_category wasDerivedFrom Tannakian_category?oldid=599893295.
- Tannakian_category isPrimaryTopicOf Tannakian_category.