Given a category C, consider the category whose objects are morphisms
of C  and whose morphisms are commuting diagrams, i.e., a morphism
from h:A --> B  to g: C --> D  is a pair of morphism 

f: A --> C and k: B --> D  such that the obvious diagram
commutes. Write out the details here, show that it is a category, show
that there exists two functors dom, codom  mapping a map to its domain
and codomain respectively,  and show that there exists a natural
transformation from dom  to codom.