Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 113 / 1 / c / Solution

Use the counit from part b for the first map and the restriction map $\mathcal{G}\to i_{\ast }{i}^{-1}\mathcal{G}$ for the second. Exactness can be checked on stalks. At $P\in U$ the sequence iswhereas at $P\in Z$ it isThusis a short exact sequence of sheaves.