7 problems

Let $\operatorname{SpHorn}$ be the set of special horn inclusions. A map of simplicial sets is bijective on $0$-simplices when it induces a bijection on its sets of $0$-simplices.…

Let $\operatorname{IH}$ be the set of inner horn inclusions, and let $\operatorname{SpOH}$ be the set of special outer horn inclusions. A map of simplicial sets is bijective on $0$…

For simplicial sets $A$ and $B$, let $\mathbf{Cyl}(A,B)$ be the category of cylinders from $A$ to $B$. Thus an object is a simplicial set $X$ equipped with a map $X\to\Delta[1]$ wh…

Ara's conjecture. A $2$-functor $F$ is a biequivalence if and only if $N_sF$ is a weak equivalence in the model structure for $2$-quasi-categories.

Let $Q$ be a quasi-category tensored and cotensored over $\mathfrak N[\mathcal{K}\!\mathit{an}]$, let $d\colon J\to Q$ be a diagram, and let $p\colon\tilde J\to J$ be a weight. Let…

Let $Q$ be a quasi-category, let $d\colon J\to Q$ be a diagram, and let $p\colon\tilde J\to J$ be a weight. Write $st(p)^{bifib}\colon J\to\mathfrak N[\mathcal{K}\!\mathit{an}]$ fo…

A higher quasi-category is a model for an $(\infty,n)$-category, and a Rezk $\Theta_n$-space is another model for an $(\infty,n)$-category. The $\Theta_n$-localizer is the localize…