A sheaf of abelian groups is injective if every morphism to it from a subsheaf extends to the containing sheaf. Every such sheaf embeds in an injective sheaf. Injective sheaves are flasque: the inclusion of extension by zero constant-integer sheaves associated to turns the extension property into surjectivity of restriction from to .
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In algebraic geometry and sheaf theory, an **injective sheaf** is a type of sheaf that has properties analogous to those of injective modules in the category of modules. To understand injective sheaves, it's useful to consider their role in the context of sheaf theory and derived functors.