Is there any work on compactifications of spaces in terms of category theory? I would like to know whether there is a defined category of compactifications; I will denote it Comp.
- Could you describe Comp like this?
- Objects = compactifications
- Morphisms = homeomorphisms between compactifications?
- Also, intuitively a Stone-Čech compactification is a "biggest" object and an Alexandroff compactification is a "smallest" object of Comp. Would they have any special properties then? I.e. would they be initial and terminal objects respectively?
Thank you for your insights.