## Tag `08WY`

Chapter 34: Descent > Section 34.4: Descent for universally injective morphisms

Definition 34.4.15. The functor $f^*: \text{Mod}_R \to DD_{S/R}$ is called

base extension along $f$. We say that $f$ is adescent morphism for modulesif $f^*$ is fully faithful. We say that $f$ is aneffective descent morphism for modulesif $f^*$ is an equivalence of categories.

The code snippet corresponding to this tag is a part of the file `descent.tex` and is located in lines 1092–1099 (see updates for more information).

```
\begin{definition}
\label{definition-effective-descent}
The functor $f^*: \text{Mod}_R \to DD_{S/R}$
is called {\it base extension along $f$}. We say that $f$ is a
{\it descent morphism for modules} if $f^*$ is fully
faithful. We say that $f$ is an {\it effective descent morphism for modules}
if $f^*$ is an equivalence of categories.
\end{definition}
```

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