Injective object

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One talks about injective objects in categories more general than module categories, for instance in functor categories or in categories of sheaves of OX modules over some ringed space (X,OX). The following general definition is used: an object Q of the category C is injective if for any monomorphism f : X → Y in C and any morphism g : X → Q there exists a morphism h : Y → Q with hf = g.

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