Exercise 4-31

Prove that the serial composition of profunctors, \(\mathcal{X}\overset{\phi}\nrightarrow\mathcal{Y}\) and \(\mathcal{Y}\overset{\psi}\nrightarrow\mathcal{Z}\), is associative.

Solution(1)

This is tantamount to the quantale matrix multiplication being associative, which was shown in Exercise 2.104.