4 problems

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…

Let $\{x\}\to\mathcal{H}$ be a map in the set (A2) from Bergner's simplicial categories model-structure construction. Let $L$ denote the relevant left adjoint, and suppose that the…

Let $\mathbf{Cyc}(\mathbf{sSet})$ denote the category of cyclic operads enriched in simplicial sets. An unpositive Dwyer–Kan model structure conjecture. The category…

Let $\mathcal{P}$ be an operad and let $\mathcal{A}_\infty\to\mathcal{P}$ be a morphism that lifts to the category of non-$\Sigma$ cyclic operads. Suppose the associated deformatio…