Trying to read Lang Algebra. But, can't really think as I'm ill and my head hurts.
But, I don't understand the definition of commutativity diagram.
A diagram in which any two mappings between the same pair of sets, formed by composition of mappings represented by arrows in the diagram, are equal.
Surely, commutativity is the idear that order doesn't matter. But, clearly it will matter in a commutative diagram, you can't say have fp=pf.