5 problems

Let $\mathbb{M}$ be the double category governing the simplicial coloured $\mathbb{M}$-operads, and let $\Delta_{\mathbb{M}}$ be the total category of the Grothendieck construction…

Nerve completeness conjecture. The $d$-categorical nerve $I$ is a complete and discrete $d$-fold Segal space.

Let $\mathcal{V}$ be a pointed $\mathbb{E}_{n}$-monoidal $(\infty,1)$-category, meaning that its monoidal unit is the initial object. Let…

Higher-coherence conjecture for Segal types. An analogue for Segal types of the result that internal identity-elimination operations automatically provide all higher groupoid struc…

Joyal's conjecture. The internal definition of a Segal type is equivalent to the usual definition of a Segal space, in which all Segal maps