Least and largest initial completions. I.
Liftings of Stone's monadicity to spaces and the duality between the calculi of inverse and direct images
Linking the closure and orthogonality properties of perfect morphisms in a category
We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.
Local enrichments of categories