Injective object
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In category theory, an object Q is said to be injective if every arrow to Q can be pushed forward across monomorphisms. That is, Q 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.
In the category of modules and module homomorphisms, an injective object is an injective module. In the category of metric spaces and nonexpansive mappings, an injective object is an injective metric space. One also talks about injective objects in more general categories, for instance in functor categories or in categories of sheaves of OX modules over some ringed space (X,OX).
