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Inverse system

Index Inverse system

In mathematics, an inverse system in a category C is a functor from a small cofiltered category I to C. An inverse system is sometimes called a pro-object in C. The dual concept is a direct system. [1]

9 relations: Alexander Grothendieck, Category (mathematics), Direct limit, Filtered category, Fondements de la Géometrie Algébrique, Functor, Inverse limit, Mathematics, Profinite group.

Alexander Grothendieck

Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.

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Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.

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Direct limit

In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way.

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Filtered category

In category theory, filtered categories generalize the notion of directed set understood as a category (hence called a directed category; while some use directed category as a synonym for a filtered category).

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Fondements de la Géometrie Algébrique

Fondements de la Géometrie Algébrique (FGA) is a book that collected together seminar notes of Alexander Grothendieck.

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Functor

In mathematics, a functor is a map between categories.

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Inverse limit

In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Profinite group

In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups.

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Redirects here:

Ind-object, Pro-category, Pro-object.

References

[1] https://en.wikipedia.org/wiki/Inverse_system

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