Editing Injective module (section)

=== Injective objects ===

{{Main|injective object}}
One also talks about [[injective object]]s in [[category (mathematics)|categories]] more general than module categories, for instance in [[functor category|functor categories]] or in categories of [[sheaf (mathematics)|sheaves]] of O<sub>''X''</sub>-modules over some [[ringed space]] (''X'',O<sub>''X''</sub>). 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''.