15 problems

Constructor-space factorization conjecture. All theorems of $L$ can be realized as actual factorizations in $\operatorname{CatTh}[E_L,\mathcal{F}]$.

Let $\mathbf{S}$ be the equational calculus whose axioms are the axioms of commutative monoids with respect to $\wedge$ and $\top$, together with … and … Interpret formulae arithme…

A semi star-autonomous category is the categorical structure defined in the paper, and a proof-net category is the unitless linearly distributive category with suitable duals defin…

Sober-category characterization conjecture. The sober quasi-Polish categories are exactly the spaces of models of countable predicate $\sigma$-coherent theories, up to continuous e…

Logical relations are modeled by suitable categorical structures, and an internal fibration is a fibration defined within an appropriate 2-category of models. Internal-fibration co…

Symmetric lax monoidal Kleisli biadjunction conjecture. The Kleisli biadjunction becomes a symmetric lax monoidal biadjunction. Equivalently, it is sufficient to show that the left…

Characterization conjecture. The structures $(\mathbf{P}_0,\mathbf{P}_1)$ that are part of a QA-stratified Boolean doctrine are precisely the QA-one-step Boolean doctrines.

A topos with enough points is a topos whose points form a conservative family of geometric morphisms to the category of sets. A topos is locally finitely presentable when it is loc…

Let first-order logic theories have finite signatures. Barrett–Halvorson's conjecture. Categorical equivalence implies many-sorted (Morita) definitional equivalence. The paper prov…

Two-row matrix-class conjecture. Figure 2,3,2 shows all matrix classes induced by two-row matrices.

Let $\mathbf{K}_{3}$ denote the strong Kleene logic, and let an extensive restriction category be equipped with an additional parallel composition operator such as finite joins. St…

Forster–Lewicki–Vidrine's conjecture. Every model of $T$ has a subcategory which is a topos.

Conjecture.

Let $L$ be a logical system, let $\E_L$ be the kind of category in which the models of $L$ are, and let $\F$ be the specified target structure. Suppose that $\CatTh[\E_L,\F]$ is th…

Let $(\ct{E},\smallmap{S})$ be a category with display maps, and let $(\overline{\ct{E}},\overline{\smallmap{S}})$ denote its exact completion. The axioms ${\bf (\Pi S)}$ and…