8 problems

Extension property converse. If every $(S,\underline D)$-diagram of ${\cal P}$-algebras can be extended to an $S$-diagram of ${\cal P}$-algebras, then the couple $(S,D)$ has the…

Let ${\cal A}_{\mathfrak D}$ be the colored operad of ${\mathfrak D}$-diagrams of ${\cal A}$-algebras, let ${\cal R}_{\mathfrak D}=({\cal F}(F),d_{\mathfrak D})$ be a cofibrant res…

Let $F4(d)$ be the symmetric ribbon category generated by a trivalent vertex subject to the defining $F4(d)$ relations, and let $\operatorname{Hom}$ denote a morphism space in this…

Let $R$ be a ring and let $\mathsf{QExc}_{R,v,w}$ be the quantum exceptional diagram category, with $\mathbb Q(v,w)$-valued closed-diagram evaluations defined by the stated relatio…

Quantum sufficiency conjecture. If every polynomial in $\mathbf P$ is invertible in $R$, then the space of $n$-boundary-point diagrams in $\mathsf{QExc}_{R,v,w}$ is finitely genera…

Let $R$ be a ring and let $\mathsf{Exc}_{R,\lambda}$ be the classical exceptional diagram category, with $\mathsf{Exc}_{R,\lambda}(0)$ its closed-diagram space and the empty diagra…

Let $R$ be a ring and let $\boldsymbol{\lambda}$ be a parameter such that the category $\mathsf{Exc}_{R,\lambda}$ is defined; write $\mathsf{Exc}_{R,\lambda}(n)$ for its space of d…

Let $C$ be the category whose morphism sets are the finite diagram sets $C(k,l)$, and let $NC_2$ denote the category of non-crossing pair partitions. Let $NC_2\times NC_2$ be their…