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Tightness relative to some (co)reflections in topology
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
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
TLDR
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.
Quotients of d-Frames
TLDR
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.
Free constructions and coproducts of d-frames
TLDR
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.
University of Birmingham Free constructions and coproducts of d-frames
TLDR
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.
Classification of finite semigroups and categories using computational methods
TLDR
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.
University of Birmingham Quotients of d-Frames
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
d-Frames as algebraic duals of bitopological spaces
TLDR
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.
Some point-free aspects of connectedness
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