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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 a descent morphism for modules if $f^*$ is fully faithful. We say that $f$ is an effective descent morphism for modules if $f^*$ 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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