Simplicial mapping space ($\underline{\mathrm{Hom}}(A,X)$)

The simplicial mapping space is defined byIf $A\hookrightarrow B$ is a monomorphism and $X$ is a Kan complex, restriction $\underline{\mathrm{Hom}}(B,X)\to \underline{\mathrm{Hom}}(A,X)$ is a Kan fibration.