6 problems

Higher-dimensional polygraph conjecture. The coordinate ring of $Z(n,l)$ over $E=\mathbb{A}^d$ is a free $k[\mathbf{z}]$-module.

Let $\mathcal{S}$ be the class of molecules with spherical boundary. Algebraic freeness conjecture. The class $\mathcal{S}$ of molecules with spherical boundary is algebraically fr…

Let $P$ be a directed complex. It is freely generating when $(\mathcal{M}o\ell_{}{P})^*$ admits the structure of a polygraph whose $n$-dimensional generators are the $n$-dimensiona…

Let $\mathbf{CPol}$ be the category of constructible polygraphs and let $\mathbf{RCPol}$ be the category of representable constructible polygraphs and strong maps. For a constructi…

Let $P$ be a directed complex. Say that $P$ is freely generating if $(\mathcal{M}o\ell_{}{P})^*$ admits the structure of a polygraph whose $n$-dimensional generators are the $n$-di…

Let $\mathbf{CPol}$ be the category of constructible polygraphs, with monoidal structures given by the lax Gray product $\scaleobj{0.75}{\boxtimes}$ and the join $\star$, and let…