Detecting equivalences on mapping animae

Exercise 1.4.15. Let \(F\colon C \to D\) be a functor. Show that the following conditions are equivalent:

(1)

The functor \(F\) is an equivalence;

(2)

For every \(\infty \)-category \(E\) the functor \(F \circ -\colon \Map (E,C) \to \Map (E,D)\) is an equivalence;

(3)

For every \(\infty \)-category \(E\) the functor \(- \circ F\colon \Map (D,E) \to \Map (C,E)\) is an equivalence.