Reflective Subcategory: Ab

Ab is a reflective subcategory of Grp, by which we mean that Ab is a full subcategory whose inclusion functor has a left adjoint. The inclusion functor i is called the reflection and the left adjoint is called the reflector.

Reflectors tend to be meaningful, and in this case, the functor which reflects Grp to Ab is called the Abelianization functor of Grp.

In terms of stuff, structure, and properties, objects of Grp are like objects of Ab but with extra stuff; this is the reflection of the fact that, because Ab is a full subcategory, objects of Ab are like objects of Grp but with extra properties.

reflective_subcategories: Ab, Grp

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