 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-22/5/b/iii/solution

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

ρ_{B} : B \to K B

is an isomorphism, then

B

is isomorphic in

B

to an object of

C

. Since

C

B

. Thus invertibility of the unit implies membership, completing the cycle of implications:

B \in C ⟺ [h \mapsto h ρ_{B^{'}} is bijective for every B^{'}] ⟺ ρ_{B} is invertible .

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