+* composition of morphisms, functors, and natural compositions is associative
+
+* functors "distribute over composition", that is for any morphisms `f` and `g` in `F`'s source category: <code>F(g ∘ f) = F(g) ∘ F(f)</code>
+
+* if <code>η</code> is a natural transformation from `G` to `H`, then for every <code>f:C1→C2</code> in `G` and `H`'s source category <b>C</b>: <code>η[C2] ∘ G(f) = H(f) ∘ η[C1]</code>.
+
+* <code>(η F)[E] = η[F(E)]</code>
+
+* <code>(K η)[E} = K(η[E])</code>
+
+* <code>((φ -v- η) F) = ((φ F) -v- (η F))</code>