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

source jl@crush.caltech.edu index