injective object

Object 𝑋 in an abelian category such that hom(–,𝑋) is an exact functor to the opposite category of the category of abelian groups

EntityQ1625040

Subclass of: object of a category

Overview

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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.

Overview

All data

8 statements · 13% with external sources · numbers in brackets are citations

Studied by: homological algebra
Dual notion (category theory): projective object

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5 identifiers linking injective object across the web's reference databases

Data quality

statements

13%

externally sourced

Source last edited October 8, 2026. AIDb refreshes this page daily.

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AIDb. (2026). injective object (Q1625040). Retrieved from https://aidb.si/e/injective-object-Q1625040