The Stacks project

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

  1. $R \to S$ is an epimorphism,

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

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

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

Proof. Omitted. $\square$

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