10 problems

Let $K$ be an algebraically closed field and let $C$ be a $K$-coalgebra. The coalgebra $C$ is of tame comodule type if its finite-dimensional indecomposable comodules are parametri…

Inverse-limit comparison conjecture. The map above is an isomorphism of the cohomology groups.

Comparison conjecture. There is an isomorphism of homology theories

Let $\mathsf{T}_{\mathsf{INC}}$ denote the tangent endofunctor on $\mathsf{INC}(\mathcal{C})$, and suppose either preceding existence theorem applies, so that the universal Lincs c…

Let $H$ be a non-cosemisimple Hopf algebra over $\Bbbk$ with the dual Chevalley property. Let $\mathcal{M}$ denote the set of simple subcoalgebras of $H$, and let $\mathcal{P}$ be…

Let $T\colon n\mapsto n+1$ be a Poisson map admitting a coalgebra symmetry $(\mathfrak{A},\Delta)$. Let the generators of the coalgebra symmetry satisfy the closure relation referr…

Simson's infinite tame-wild dichotomy conjecture. Every coalgebra $C$ is either tame or wild, but not both.

Let $H$ be a connected Hopf algebra of finite Gelfand–Kirillov dimension, with antipode $S$. The Nakayama automorphism conjecture. The Nakayama automorphism of the coalgebra $H$ is…

Let $\mathbf{Grp}$ be the category of groups, let $\mathbf{Zinb}^c$ denote coZinbiel coalgebras, and let $\mathbf{Com}^c$ denote cocommutative coalgebras. For a group $G$, write…

Let $H$ be a co-Frobenius Hopf algebra, meaning that it has a nonzero left integral (equivalently, any of the equivalent conditions characterizing co-Frobenius Hopf algebras). Its…