8 problems

The paper concerns algebras over a prop in chain complexes of vector spaces, and considers analogous homotopical and model-categorical constructions for simplicial modules. Simplic…

The graphs defined by Kontsevich form a Feynman PROP $K$, and let $F$ denote the forest PROP introduced above. Freeness conjecture. The PROP $K$ is conjectured to be the free PROP…

Let $\mathcal{H}$ be the bialgebra object, let $\mathcal{H}_{\infty}$ be the canonical differential graded submodule resolving its prematrad version…

Koszul bar-to-levelled conjecture. The composition

Bar-to-levelled construction conjecture. The morphism $e$ is a quasi-isomorphism.

Let $\mathcal{E}_\Lambda^\bullet$ be the category whose objects are indexed by nonnegative integers, with morphisms represented by the elements $\rho_\lambda$ associated to partiti…

Let $\mathbb{L}_{\scriptscriptstyle \Sigma_{\scriptscriptstyle M},E_{\scriptscriptstyle M}}$ be the PROP of linear systems, and let $\mathbb{C}$ and $\mathbb{M}$ be the PROPs of co…

Let $\mathrm{Fin}\mathrm{Corel}^{\circ}$ be the symmetric monoidal subcategory of $\mathrm{Fin}\mathrm{Corel}$ generated by the morphisms associated to the two Frobenius monoids on…