# PlanetPhysics/Grothendiecks Theorem

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\begin{theorem}

{\mathbf Grothendieck's theorem}:
*Every category with a generator has an injective cogenerator* (Grothendieck 1957).
\end{theorem}

This initial statement of Grothendieck's theorem is now restated as: \begin{theorem} Every Grothendieck category has an injective cogenerator. \end{theorem}