Giraud subcategory

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

Definition

Let \mathcal{A} be a Grothendieck category. A full subcategory \mathcal{B} is called reflective, if the inclusion functor i\colon\mathcal{B}\rightarrow\mathcal{A} has a left adjoint. If this left adjoint of i also preserves kernels, then \mathcal{B} is called a Giraud subcategory.

Properties

Let \mathcal{B} be Giraud in the Grothendieck category \mathcal{A} and i\colon\mathcal{B}\rightarrow\mathcal{A} the inclusion functor.

See also

References

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