## Recall:

Given a category $A$, and two classes of morphisms $S,S'$, we say that $S$ is *right-cancellative with respect to $S'$* if for any pair of maps $f\in S, g\in S'$ such that $gf$ is defined, we have the implication $gf\in S \Rightarrow g\in S$.

Recall that the class of inner-anodyne morphisms in the category of simplicial sets is defined to be the class $\operatorname{llp}(\operatorname{rlp}(E))$, where $E$ denotes the set of inner-horn inclusions $\iota^n_k:\Lambda^n_k \hookrightarrow \Delta^n$ for $0<k<n.$

## Question:

Is the class of inner-anodynes right-cancellative with respect to the class of monomorphisms? This is certainly the case for the Joyal-trivial cofibrations, but being inner-anodyne is a rather stronger condition.