The Stacks project

Situation 38.25.1. Let $\varphi : A \to B$ be a local ring homomorphism of local rings which is essentially of finite type. Let $M$ be a flat $A$-module, $N$ a finite $B$-module and $u : N \to M$ an $A$-module map such that $\overline{u} : N/\mathfrak m_ AN \to M/\mathfrak m_ AM$ is injective.