Recall:
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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:
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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. 



Is the class of inner-anodyne morphisms right-cancellative with respect to the of the class of monomorphisms?
The fact that in $\operatorname{Set}\_{\Delta}$ the class of inner anodyne maps has the right cancellation property (within the class of monomorphisms) was proven by Danny Stevenson in his 2016 paper [*Stability for inner fibrations revisited*](https://arxiv.org/abs/1608.07699), which was also published in [*TAC*](http://www.tac.mta.ca/tac/volumes/33/19/33-19abs.html).


