A characterization of locally -presentable categories
A convenient category for directed homotopy.
A duality relative to a limit doctrine.
A logic of injectivity.
A logic of orthogonality
A logic of orthogonality characterizes all “orthogonality consequences" of a given class of morphisms, i.e. those morphisms such that every object orthogonal to is also orthogonal to . A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes of morphisms such that all members except a set are regular epimorphisms and (b) for all classes , without...
Algebraically closed and existentially closed substructures in categorical context.