 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-22/6/c/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

μ

is invertible, the two unit identities of the monad

μ \circ T η = 1_{T}, μ \circ η T = 1_{T}

make both

T η

and

η T

its inverse. Hence idempotence implies equality of the two unit insertions:

T η = η T = μ^{- 1} .

This is the first implication in the characterization of an idempotent monad.

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