On extended frames
Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.
On extensions of full embeddings and binding categories
On functors which are lax epimorphisms.
On fuzzification of the notion of quantaloid
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of -semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At...
On generalized Hom-functors of certain symmetric monoidal categories
On generic separable objects.
On hereditary and product-stable quotient maps
It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.
On ideals and homology in additive categories.
On invariant multiplications in a category
On Inverse Limit Of Function Spaces
On limits and colimits in the Kleisli category
On Mackey topologies in topological abelian groups.
On product and change of base for toposes
On projectiveness in H-closed spaces
On property-like structures.
On pure quotients and pure subobjects
In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.
On rich monoids
On saturated classes of morphisms.
On sifted colimits and generalized varieties.
On simply bireflective subcategories