Abstract We address what might be termed the reverse reflection problem: given a monoreflection from a category A onto a subcategory B, when is a given object B ∈ B the reflection of a proper… Expand

This work focuses on the use of topological duality methods and category theory and, more particularly, free (and co-free) constructions, to unify the `power' and `structure' strands in computer science.Expand

It is shown that every d-frame admits a complete lattice of quotients, and it will be that both frames are factored and both consistency and totality are increased.Expand

It is proved that the category of d-frames is closed under coproducts and the difficulties are reviewed and sufficient conditions for when they can be overcome.Expand

As an application it is proved that the category of d-frames is closed under coproducts, and it is reviewed the difficulties and gives sufficient conditions for when they can be overcome.Expand

This work relies on the use of McCune’s Prover9/Mace4 to construct models, providing in particular a count of the number of categories with two non-isomorphic objects and such that all hom-sets have size 3.Expand

It is shown that every d-frame admits a complete lattice of quotients. Quotienting may be triggered by a binary relation on one of the two constituent frames, or by changes to the consistency or… Expand

Basic categorical properties of d-frames are investigated, a Vietoris construction for d- frames is given which generalises the corresponding known Vietoris constructions for other categories, and the connection between bispaces and a paraconsistent logic is investigated and developed.Expand