On categorical notions of compact objects (Q1364906)

The concept of compactness has found various categorical generalizations. In this paper the author studies two such -- seemingly unrelated -- concepts: Borel-Lebesgue-compactness, based on the concept of a closure operator, an Áhn-Wiegandt-compactness, based on the bahaviour of certain morphisms with respect to projective limits. The main result establishes that in convenient settings each Áhn-Wiegandt-compactness is a Borel-Lebesgue-compactness.