5 problems

Dendroidal sets form a category equipped with a notion of inner Kan complex; for dendroidal sets $X$, $Y$, and any dendroidal inner Kan complex $K$, write…

Let $\Omega_{cyc}^{\Sigma}$ be the category of symmetric unrooted trees, and let $\operatorname{Fun}((\Omega_{cyc}^{\Sigma})^{\operatorname{op}},\mathbf{sSet})$ denote the category…

Quillen-equivalence conjecture. There exists a model structure on $\mathsf{dSet}_G$ for which this adjunction is a Quillen equivalence.

Weak equivalence conjecture. The inclusion of simplicial sets $N(ubi\mathcal{C}tg)\longrightarrow i^*(w\mathcal{C}at^2)$ is a weak equivalence in the Joyal model structure on…

Let $n\ge 0$ be fixed. For $k\ge 0$, define recursively the dendroidal set $wCat_k^n$ of weak $k$-monoidal $n$-categories by … and, for $k>0$, … A dendrex of shape $\eta$ in…