PlanetPhysics/Grothendieck's Theorem

\newcommand{\sqdiagram}[9]{Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

\begin{theorem}

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