**Puzzle 168**

So the 2 morphisms are :

$$\alpha_{a',b'}(g \circ h \circ F(f))$$
$$G(g) \circ \alpha_{a,b}(h) \circ f$$

Now check if these two are equal using the fact that \$$\alpha_{a,b}\$$ is like taking \$$G\$$ and \$$G(F(h)) = h \$$ :

$$\alpha_{a',b'}(g \circ h \circ F(f))$$
$$= G(g \circ h \circ F(f))$$
$$= G(g) \circ G(h) \circ f$$
$$= G(g) \circ \alpha_{a,b}(h) \circ f$$