7 problems

Let a weak $n$-category be a higher category whose composition laws are associative and unital only up to coherent invertible higher morphisms. Simpson's weak units conjecture. Any…

Let $\text{St}_1: (\infty,1)\text{Cat}\to(\omega,1)\text{Cat}$ be the strictification functor constructed by locally strictifying hom $\infty$-groupoids and then strictifying the e…

Let a strict $\infty$-category be a higher category in which composition, associativity, and the exchange law are strict. Consider the weaker structures obtained by replacing stric…

Let $\mathrm{St}_1:(\infty,1)\text{Cat}\to(\omega,1)\text{Cat}$ be the strictification functor, left adjoint to a natural inclusion functor. For a functor…

A bipermutative category has additive and multiplicative symmetric permutative structures, with the multiplicative structure distributing over the additive one. A symmetric bimonoi…

Pseudoadjunction conjecture. There is a pseudoadjunction between the locally discrete 2-category of bicategorical graphs and the 2-category of bicategories, pseudofunctors and icon…

For an integer $m$, let $\mathbf{sSet}^m$ denote the category of stratified simplicial sets and let $\infty\text{-}\mathbf{Cat}^m$ denote the category of marked strict $\infty$-cat…