Reflective Subcategory: CompMet

CompMet is a reflective subcategory of Met, by which we mean that CompMet 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 Met to CompMet is called the Cauchy completion functor of Met.

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

reflective_subcategories: CompMet, Met

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