4 problems

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…

Regularity conjecture. Every regular directed complex should be freely generating, meaning that $(\mathcal{M}o\ell_{}{P})^*$ admits a polygraph structure whose $n$-dimensional gene…

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 $1\leqslant n\leqslant\infty$. Consider the Street nerve from strict $n$-categories to simplicial sets, and the nerve functor from augmented directed complexes to simplicial se…