Finding the maximum area of isosceles triangle

ct.class idea – query about notation in HTT of J.Lurie Answer

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ct.class idea – query about notation in HTT of J.Lurie

In web page 27 in HTT of J.Lurie, the expression
$$textual content{Map}_S(X,Y):=Y^Xtimes_{S^X}{phi}in textual content{Set}_Delta$$
seems for simplicial clique $X,Y,S$ in Warning 1.2.2.2. However, I could not grasp two notation on this expression, first one is exponential of simplicial clique and the second is product which have scowl index. I speculate that $X^Y$ is kindly of $Hom_{textual content{Set}_Delta}(X,Y)$, however I could not breathe positive about it.

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