Definition 59.16.5. Let $A \to B$ be a ring map and $N$ a $B$-module. A *descent datum* for $N$ with respect to $A \to B$ is an isomorphism $\varphi : N \otimes _ A B \cong B \otimes _ A N$ of $B \otimes _ A B$-modules such that the diagram of $B \otimes _ A B \otimes _ A B$-modules

commutes where $\varphi _{01} = \varphi \otimes \text{id}_ B$ and similarly for $\varphi _{12}$ and $\varphi _{02}$.

## Comments (2)

Comment #1702 by Yogesh More on

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