Functoriality of loops and suspensions

Exercise 2.4.7. Show that the assignments \(X \mapsto \Omega X\) and \(X \mapsto \Sigma X\) define endofunctors \[ \Omega , \Sigma \colon \An _* \to \An _*. \] Hint: Use the pushout description of the diagram \(\pullback \) from Axiom D to construct a functor \(C \to \Fun (\pullback ,C)\) given on objects by \(X \mapsto (0 \to X \leftarrow 0)\).