TestUt8 2026-08-16 02:49:38 2026-08-16 02:49:38 Definition % this is the default PhysicsLibrary preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \begin{theorem} {\bf 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}