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Injective object

In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in cohomology, in homotopy theory and in the theory of model categories. The dual notion is that of a projective object.

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Overview

Definition

In Abelian categories

Enough injectives and injective hulls

Examples

Uses

Generalization

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Injective object

Nodes62
Edges61
Triples34
Avg. degree1.97
Density0.032258
Components1

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Injective object

Top relations

related to References · 19
Injective object → Abstract, Applications, Cagliari, Categories, Chapter, Essential Embeddings, George Strecker, Horst Herrlich, Injective Objects, Injectivity, Jiri Adamek, Montovani, No, Reprints, Republished, Rosicky, T0-reflection, The, Wiley
related to Examples · 7
Injective object → Ab, Assuming, In, Met, R-Mod, Scott, T0
related to Examples of .mw-parser-output .mathcal{font-family:"Lucida Calligraphy","Monotype Corsiva","URW Chancery L","Apple Chancery","Tex Gyre Chorus",cursive,serif}H-injective objects · 4
Injective object → Dedekind, In, Kan, MacNeille
is a · 3
Injective object → generalization of the concept of injective module, injective metric space, injective module
related to Enough injectives and injective hulls · 1
Injective object → The

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Important terminology

injective category object displaystyle mathbf mathcal morphism categories monomorphism abelian enough objects class every hull theory injectives said exists functor

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Injective objectis ageneralization of the concept of injective module0.90text
Injective objectis ainjective module0.90text
Injective objectis ainjective metric space0.90text
Injective objectrelated to Enough injectives and injective hullsThe0.60section
Injective objectrelated to ExamplesIn0.60section
Injective objectrelated to ExamplesAb0.60section
Injective objectrelated to ExamplesAssuming0.60section
Injective objectrelated to ExamplesR-Mod0.60section
Injective objectrelated to ExamplesMet0.60section
Injective objectrelated to ExamplesT00.60section
Injective objectrelated to ExamplesScott0.60section
Injective objectrelated to Examples of .mw-parser-output .mathcal{font-family:"Lucida Calligraphy","Monotype Corsiva","URW Chancery L","Apple Chancery","Tex Gyre Chorus",cursive,serif}H-injective objectsIn0.60section

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