Composition on hom animae

Exercise 1.4.19. Let \(x\), \(y\) and \(z\) be objects of an \(\infty \)-category \(C\). Construct a composition functor \[ - \circ - \colon \Hom _C(y,z) \times \Hom _C(x,y) \to \Hom _C(x,z), \qquad (g,f) \mapsto g \circ f. \] Hint: Restrict the composition functor \(\Ar (C)\times _{s,C,t}\Ar (C)\to \Ar (C)\) along the pullbacks defining the three hom animae.