The following paper may be requested from Maria Manuel Clementino (paper or electronic copy) by writing to clementino@gemini.ci.uc.pt "Compact objects and perfect morphisms" by M.M. Clementino, E. Giuli and W. Tholen Abstract: In a category with a subobject structure and a closure operator, we provide a categorical theory of compactness and perfectness which yields a number of classical results of general topology as special cases, including the product theorems by Tychonoff and Frolik and the existence of Stone-Cech compactifications, both for spaces and maps. Applications to other categories are also provided.