In the category of pointed simplicial sets, we have an adjunction between smash product and mapping space.
We define mapping space as follows:
$\textbf{Map}_*(X,Y)_n$ := $Hom_{sSets_*}(X \wedge \triangle_{+}^{n} , Y)$
It would be helpful if someone could provide me with some intuition to think about $\textbf{Map}_*(X,Y)$. What is the geometric realization of this?