-(*
- P2. every element c1 of a category C has an identity morphism id[c1] such that for every morphism f:c1->c2 in C: id[c2] o f = f = f o id[c1].
- P3. functors "preserve identity", that is for every element c1 in F's source category: F(id[c1]) = id[F(c1)].
-*)
+ (ii) (ρ <=< γ) <=< φ = ρ <=< (γ <=< φ)
+
+ (iii.1) (unit G') <=< γ = γ
+ when γ is a natural transformation from some FG' to MG'
+
+ (iii.2) γ = γ <=< (unit G)
+ when γ is a natural transformation from G to some MR'G
+</pre>
+
+
+
+Getting to the standard category-theory presentation of the monad laws
+----------------------------------------------------------------------
+In category theory, the monad laws are usually stated in terms of `unit` and `join` instead of `unit` and `<=<`.
+
+<!--
+ P2. every element C1 of a category <b>C</b> has an identity morphism 1<sub>C1</sub> such that for every morphism f:C1→C2 in <b>C</b>: 1<sub>C2</sub> ∘ f = f = f ∘ 1<sub>C1</sub>.
+ P3. functors "preserve identity", that is for every element C1 in F's source category: F(1<sub>C1</sub>) = 1<sub>F(C1)</sub>.
+-->