A commutative diagram can occur when there are 2 compositions leading to 
the same set.


f:X->Y and g:Y->Z => h:X->Z with h=gf
j:X->W and k:W->Z => i:X->Z with i=kj

The commutative diagram looks like:
   f	
 X -> Y
j|    |g
 "    "
 W -> Z
   k