Classically, a Tychonoff space is called strongly 0-dimensional if its Stone-Čech compactification is 0-dimensional, and given the familiar relationship between spaces and frames it is then natural to call a completely regular frame strongly 0-dimensional if its compact completely regular coreflection is 0-dimensional (meaning: is generated by its complemented elements). Indeed, it is then seen...

We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized as a coreflection, i.e. the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of...

It is shown that for any commutative unital ring R the category HopfR of R–Hopf algebras is locally presentable and a coreflective subcategory of the category BialgR of R–bialgebras, admitting cofree Hopf algebras over arbitrary R–algebras. The proofs are based on an explicit analysis of the construction of colimits of Hopf algebras, which generalizes an observation of Takeuchi. Essentially be ...

We prove that in the category of achimedean lattice-ordered groups with weak unit there is no homomorphism-closed monoreflection strictly between the strongest essential monoreflection (the so-called “closure under countable composition”) and the strongest monoreflection (the epicompletion). It follows that in the category of regular σframes, the only non-trivial monoreflective subcategory that...

Classically, a Tychonoff space is called strongly 0-dimensional if its Stone-Čech compactification is 0-dimensional, and given the familiar relationship between spaces and frames it is then natural to call a completely regular frame strongly 0-dimensional if its compact completely regular coreflection is 0-dimensional (meaning: is generated by its complemented elements). Indeed, it is then seen...

We introduce the notion of strong concatenable process for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a functor Q[ ] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories with free non-commutative monoids of objects, in the precise sense that, for each net N , the strong...

This paper looks at the design process of the WamBam; a selfcontained electronic hand-drum meant for music therapy sessions with severely intellectually disabled clients. Using coreflection with four musical therapists and literature research, design guidelines related to this specific user-group and context are formed. This leads to a concept of which the most relevant aspects are discussed, b...

The uniform box product Πμ of countably many copies of the one-point compactification of the discrete space of cardinality אμ is not weakly δθ-refinable. This is shown with the help of a closed subspace T which has a natural tree structure and is naturally homeomorphic to the space F∗ of all functions from ω1 to ω ∪ {−1} that are constantly equal to −1 on [α, ω1) and are unequal to it and one-t...

It will be convenient to call a space X a ParoviZenko space if (cy) X is a zero-dimensional compact space without isolated points, (p) every two disjoint open F,-sets have disjoint closures, and (y) every nonempty GG-set in X has non-empty interior. Compact spaces satisfying (p) are usually called F-spaces, while spaces satisfying (y) are called almost-P spaces. Examples of F-spaces are the ext...

We consider a weak version of R. L. Moore's property D. Roughly speaking, a space X is said to have property D if each discrete (in the locally finite sense) sequence of points in X can be "expanded" to a discrete family of open sets in X. A space is said to have property wD if each discrete sequence has a subsequence which can be "expanded" to a discrete family of open sets. All regular, subme...