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Inverse limit

In mathematics, an inverse limit (also called a projective limit) is a construction that allows one to "glue together" several related objects, the precise gluing process being specified by morphisms between the objects. Inverse limits can be defined in any category, although their existence depends on the category that is considered. They are a special…

Formal definition, Examples & Derived functors of the inverse limit

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Formal definition

GroupsHomomorphismsDirectedPosetFamily
29 related topics

Examples

P-adic integersModular arithmeticNatural numbersProduct topologyCylinder sets
20 related topics

Derived functors of the inverse limit

(AB4*)Left exactCountableEilenbergShort exact sequence
21 related topics

Related concepts and generalizations

Categorical dual
1 related topics

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Formal definition

Examples

Derived functors of the inverse limit

Related concepts and generalizations

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Inverse limit

Nodes85
Edges84
Triples86
Avg. degree1.98
Density0.023529
Components1

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Inverse limit

Top relations

related to References · 44
Inverse limit → Acad, Advanced Mathematics, Advances, Algebra, Amnon, An, Applications, Barry, Bourbaki, Cambridge Studies, Cambridge University Press, Categories, Chapters, Charles, Derived, Dover Publications, Gail, General, Inventiones Mathematicae, ISBN
related to Examples · 15
Inverse limit → As, Cantor, In, It, Its, Kőnig's, Let, Pro-finite, That, The, Then, This, Tychonoff's, Xi, Xm
related to Further results · 8
Inverse limit → AB4, AbI, CI, Grothendieck's, In, Jan-Erik Roos, More, The
related to Mittag-Leffler condition · 7
Inverse limit → Ai, Bourbaki, Hausdorff, If, Mittag-Leffler, Mittag-Leffler's, The
related to Derived functors of the inverse limit · 6
Inverse limit → Ab, Eilenberg, For, If, Mittag-Leffler, Specifically
related to General definition · 3
Inverse limit → Let, The, Xi
related to Related concepts and generalizations · 2
Inverse limit → More, The
is a · 1
Inverse limit → direct limit

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Important terminology

inverse limit category displaystyle morphisms system set groups limits functors mittag-leffler one natural spaces integers ij functor p-adic abelian defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Inverse limitis adirect limit0.90text
Inverse limitrelated to Derived functors of the inverse limitFor0.60section
Inverse limitrelated to Derived functors of the inverse limitIf0.60section
Inverse limitrelated to Derived functors of the inverse limitAb0.60section
Inverse limitrelated to Derived functors of the inverse limitMittag-Leffler0.60section
Inverse limitrelated to Derived functors of the inverse limitSpecifically0.60section
Inverse limitrelated to Derived functors of the inverse limitEilenberg0.60section
Inverse limitrelated to ExamplesThe0.60section
Inverse limitrelated to ExamplesThat0.60section
Inverse limitrelated to ExamplesIts0.60section
Inverse limitrelated to ExamplesPro-finite0.60section
Inverse limitrelated to ExamplesLet0.60section

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