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 homotopy theory and in theory of model categories. The dual notion is that of a projective object.

Let ${\displaystyle {\mathfrak {C}}}$ be a category and let ${\displaystyle {\mathcal {H}}}$ be a class of morphisms of ${\displaystyle {\mathfrak {C}}}$.

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