7 problems

Let $n e 1$ and assume the canonical model structure exists on $operatorname{Mod}(IC{n+1})$. Let $0leq k<n$, let $X:IC{n+2}toSet$ be a model, and let $f:D^kto UX$ be a map. Suppose…

Let $M$ be a smooth manifold, let $D(U,M)_2$ denote the relevant smooth $2$-simplices over $U$, and let $D(\mathbb{A}^n,D(U,M)_2)_1$ denote the corresponding smooth $1$-simplices.…

A $\mathbb{N}$-graded $Q$-manifold is a $Q$-manifold whose grading is by the nonnegative integers, and a Lie $n$-groupoid is the corresponding higher Lie-groupoid object. Ševera's…

Higher integration conjecture. In the category of $L_\infty$-algebroids over Lie infinity-groupoids, $\mathfrak{g}$ is Morita equivalent to $\Pi_{\infty}(\mathfrak{g})$. More gener…

Higher smooth homotopy hypothesis. Lie $n$-algebroids up to $n$-equivalence are equivalent to source $n$-connected Lie $n$-groupoids up to equivalence. In particular, generalized…

Framing conjecture. Any manifold diagram of $k$-morphisms in $X$ has a deformation-equivalent representative that admits framing on all its submanifolds, treating each generator to…

Let Batanin's $n$-groupoids denote the higher groupoid models constructed using his globular operad, and let an $n$-type be a homotopy type with no nontrivial homotopy groups above…