hi guys, this is an elementary fact but I can't understand if it is true or not. Suppose that Z is contractible, for example a cube. Suppose A is a (infinite dimensional!) sufficiently regular space. Fix a basepoint $z_0 \in Z$. Is the evaluation-in-$z_0$ map $Hom(Z,A) \to A$ an acyclic fibration? Note that is not the "tautological hom" that one can prove via adjunctions: it's the ugly one :(