Lemma 10.107.1. Let $R \to S$ be a ring map. The following are equivalent

$R \to S$ is an epimorphism,

the two ring maps $S \to S \otimes _ R S$ are equal,

either of the ring maps $S \to S \otimes _ R S$ is an isomorphism, and

the ring map $S \otimes _ R S \to S$ is an isomorphism.

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