8 problems

Let $\mathcal{V}$ be a presentable, closed monoidal $\infty$-category. Write $\operatorname{Cat}^{\mathcal{V}}$ for the $\infty$-category of $\mathcal{V}$-enriched categories and…

The direct sum axiom for operator spaces is not naturally expressed solely through the enriched category theory of modules. Enriched algebraic theory conjecture. There should exist…

Enriched generalisation conjecture. Our analysis of dinaturals can be developed in more generality by taking enriched categories over a sufficiently structured base of enrichment a…

Enriched profunctor conjecture. (Enriched) categories, (enriched) functors and (enriched) profunctors assemble into a univalent weak double category, but not into a univalent doubl…

Frobenius-monoid conjecture. The star-autonomous structure on $\int Q$ is the structure of a Frobenius monoid in $[\mathsf{C},\mathsf{SLatt}]$.

Let $T$ be a monad on $\operatorname{Set}$ and let $\mathcal{V}$ be a quantale. Write $T\mathcal{V}\operatorname{Prof}$ for the locally thin bicategory associated with…

Let $\mathcal{V}$ be a presentable, closed monoidal $\infty$-category and let $\mathcal{C}$ be a $\mathcal{V}$-enriched category. Let…

Let $\mathbb{T}=\mathbb{M}$ be the free-monoid monad, let $\mathcal{V}$ be a category equipped with the monoidal structure $(X_1,\ldots,X_n)\mapsto X_1\otimes\dots\otimes X_n$, and…