Reflective Subcategory: CRing

CRing is a reflective subcategory of Ring, by which we mean that CRing 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 Ring to CRing is called the Abelianization functor of Ring.

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

reflective_subcategories: CRing, Ring

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