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@@ -94,7 +94,7 @@ and transitive, so in $\ca C/U$ we have the isomorphism
94$$(G\times U)\times_U (X\times U) \iso (X\times U) 94$$(G\times U)\times_U (X\times U) \iso (X\times U)
95\times_U (X\times U)$$ 95\times_U (X\times U)$$
96and $(G\times U)\times_U(X\times U) = (G\times X)\times U$ and $(X\times 96and $(G\times U)\times_U(X\times U) = (G\times X)\times U$ and $(X\times
97U)\times_U (X\times U)$ because pullback preserves products. So, $G\times X\to 97U)\times_U (X\times U) = (X\times X)\times U$ because pullback preserves products. So, $G\times X\to
98X\times X$ is a local isomorphism, hence an isomorphism. 98X\times X$ is a local isomorphism, hence an isomorphism.
99 99
100[^1]: Saunders Mac Lane, Ieke Moerdijk. Sheaves in geometry and logic. Springer, 1994. ISBN: 0-387-97710-4 100[^1]: Saunders Mac Lane, Ieke Moerdijk. Sheaves in geometry and logic. Springer, 1994. ISBN: 0-387-97710-4