+<pre>
+ (1) join[C2] ∘ MM(f) = M(f) ∘ join[C1]
+</pre>
+
+Next, consider the composite transformation <code>((join MG') -v- (MM γ))</code>.
+
+* <code>γ</code> is a transformation from `G` to `MG'`, and assigns elements `C1` in <b>C</b> a morphism <code>γ\*: G(C1) → MG'(C1)</code>. <code>(MM γ)</code> is a transformation that instead assigns `C1` the morphism <code>MM(γ\*)</code>.
+
+* `(join MG')` is a transformation from `MMMG'` to `MMG'` that assigns `C1` the morphism `join[MG'(C1)]`.
+
+Composing them:
+
+<pre>
+ (2) ((join MG') -v- (MM γ)) assigns to `C1` the morphism join[MG'(C1)] ∘ MM(γ*).
+</pre>