Crash Monad Tutorial

A monad in category C is an endofunctor F: C → C with two natural transformations:
u: 1 → F and m: F ∘ F → F.
Let's denote F(u): F -> F ∘ F the transformation that results in applying F to u, and F(m) : (F ∘ F) ∘ F → F ∘ F.
Having these, now we can write down the following two monad axioms:

F(u) ∘ m is identity F → F

F(X)	F(u_{_X})	F(F(X))	m_{_{_F(X)}}	F(X)
	→		→

F(m) ∘ m is the same as m ∘ m:

F(F(F(X)))	F(m_{_{_X}})	F(F(X))
	—→
m_{_{_F(X)}}↓		↓m_{_{_X}}
F(F(X))	—→	F(X)
	m_{_{_X}}