Giraud subcategory

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In mathematics, Giraud subcategories form an important class of subcategories of Grothendieck categories. They are named after Jean Giraud.

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Definition

Let be a Grothendieck category. A full subcategory is called reflective, if the inclusion functor has a left adjoint. If this left adjoint of also preserves kernels, then is called a Giraud subcategory.

Properties

Let be Giraud in the Grothendieck category and the inclusion functor.

See also

References