Local Isomorphisms Let A be a coherent analytic geometry . A fraction with a local domain is called a localization. X V is also the intersection of all the analytic subobjects of X which is not disjoint with V . X is a localization. The pullback of a local isomorphism is a local isomorphism.
T is the pullback of f along t .
We prove that s is a local isomorphism. Z is a localization of Z . X is a fraction. Also m is a fraction as a pullback of g . This shows that s is a local isomorphism.