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Exercise 31 - Chapter 4

Prove Lemma 4.30. (Hint: remember to use the fact that \( \mathcal{V} is skeletal.)

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Lemma 4.30

Serial composition of profunctors is associative: given profunctors \( \Phi : \mathcal{P} \rightarrow \mathcal{Q} \), \( \Psi : \mathcal{Q} → \mathcal{R} \), and \( \Upsilon : \mathcal{R} → \mathcal{S} \), we have $$ (\Phi.\Psi).\Upsilon = \Phi.(\Psi.\Upsilon) $$

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