In my Homological Algebra class we have defined and studied a lot of things through commutative diagrams. However, when we got to defining chain homotopies, we had to add a descriptive statement beyond "the diagram commutes".
Wikipedia does the same thing, saying that we require $f-g = d_B h + h d_A$ and putting up:
Is there a way to read off this condition directly from the diagram, or to add information to the diagram directly so that the addition and subtraction can be read off of it?