Reflective Subcategory: Comp

Comp is a reflective subcategory of Top, by which we mean that Comp 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 Top to Comp is called the Stone–Čech compactification functor of Top.

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

reflective_subcategories: Comp, Top

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