PlanetPhysics/Grothendiecks Theorem

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\begin{theorem}


{\mathbf Grothendieck's theorem}: Every ${\displaystyle {\mathcal {A}}b5}$ 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 ${\displaystyle {\mathcal {G}}}$ has an injective cogenerator. \end{theorem}