>First use \\(f: a' \to a\\) to cook up a map

>\[ \mathcal{B}(F(a),b) \to \mathcal{B}(F(a'),b) . \]

What is happening to cause a morphism,

\\[f: a' \to a\\]

to be flipped backward when being mapped to,

\[\mathcal{B}(F(f),b) : \mathcal{B}(F(a),b) \to \mathcal{B}(F(a'),b) ? \]