Homology, Homotopy and Applications
Volume 1 (1999)
A categorical guide to separation, compactness and perfectness
Pages: 147 – 161
Based on a rather arbitrary class of morphisms in a category, which play the role of “closed maps”, we present a general approach to separation and compactness, both at the object and the morphism levels. It covers essential parts of the classical topological theory, generalizes various previous categorical treatments of the theme, and allows for a number of less expected applications outside topology.
separated object, compact object, embeddable object, absolute object, perfect morphism
2010 Mathematics Subject Classification
18A40, 18B30, 54B30