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@AndreaGagna, a morphism between two operads $f:A\rightarrow B$ is a weak equivalence (fibration) if $f_{n}: A(n)\rightarrow B(n)$ is a weak equivalence (fibration) of simplicial sets for any $n$.
Sorry for my ignorance :) I did not understand what do you mean by $S^{Top}(X)$ ? What is $Aut(X)$ ? is it the group $\pi_{0}$ of the space of self equivalences of $X$, thank you.