11 problems

Let $X$ and $L$ be continuous domains, and let $T$ denote the domain used in the Scott function spaces $[X\to T]$ and $[T\to L]$. The paper considers finite-layer truncation maps a…

Let $\mathbb{F}$ be the pseudomonad whose discrete pseudoalgebras are continuous lattices, and let $\mathbf{PsAlg}_{\operatorname{ps}}(\mathbb{F})$ denote its category of pseudoalg…

Sharpness and maximality conjecture. The strongly maximal elements of $\mathcal R$ coincide with the elements that are both sharp and maximal only if a constructive taboo holds.

Strongly maximal elements conjecture. The strongly maximal elements of $\mathcal R$ coincide with the elements that are both sharp and maximal only if a constructive taboo holds.

Let $\mathsf{Infosys}$ be the category of infosys, and consider the upper powerlocale on this category. A continuous meet semilattice is a continuous domain with finite meets. Vick…

Let $\mathsf{Infosys}$ be the category of infosys, let $\mathsf{ContLat}$ be the category of continuous lattices, and consider the monad on $\mathsf{Infosys}$ arising from the lowe…

A suitable monoidal tensor and a partial additive structure on morphisms give a category the structure of a unique decomposition category, from which a trace operator can be canoni…

Let $\Xi$ be the universe of categories enriched in pointed DCPOs and Scott-continuous functors between them, respecting finite coproducts and initial objects. Let $\Theta$ be the…

Round ideal completion conjecture. For all $a,b\in P$,

Continuous-semantics conjecture. All the effective models living in the continuous semantics have non-r.e. equational theories.

Scott-semantics conjecture. No $bb$-model living in Scott's continuous semantics or in one of its refinements has an r.e. equational theory.