TestUt8 2026-08-16 02:49:38 2026-08-16 03:57:34 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 \textbf{Grothendieck's theorem}: ``Every $\mathrm{AB5}$ category with a generator has an injective cogenerator'' (Grothendieck 1957). This initial statement of Grothendieck's theorem is now restated as: Every Grothendieck category $\mathcal{G}$ has an injective cogenerator. 1. Accents This entry tests names and accents: Schr\"odinger, Noether, Poincar\'e, G\"odel, M\"obius, and na\"\i{}ve coordinate choices. The TeX-safe form is also common: Schr\"odinger, Poincar\'e, G\"odel, and M\"obius. 2. Smart Quotes This sentence uses pasted curly quotes: ``energy is conserved'' and `phase is relative'. The TeX form should also work: ``energy is conserved'' and `phase is relative'. 3. Dashes And Minus This tests dash-like characters: classical mechanics -- quantum mechanics, Hamiltonian dynamics --- Lagrangian dynamics, and the Unicode minus sign -1. The TeX forms are: classical mechanics -- quantum mechanics, Hamiltonian dynamics --- Lagrangian dynamics, and $-1$. 5. Mixed Reference A reference with correct TeX quotes: [1] Griffiths, D. ``Introduction to Quantum Mechanics'' Prentice Hall, New Jersey, 1995. A pasted Unicode version: [2] Schr\"odinger, E. ``Quantisierung als Eigenwertproblem,'' Annalen der Physik, 1926.