Talk:PlanetPhysics/Monomorphism

Original TeX Content from PlanetPhysics Archive
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: monomorphism %%% Primary Category Code: 00. %%% Filename: Monomorphism.tex %%% Version: 3 %%% Owner: bci1 %%% Author(s): bci1 %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}

\usepackage{html}

% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amsthm}

% used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions % % making logically defined graphics \usepackage{xypic}

% there are many more packages, add them here as you need them

% define commands here

\newcommand{\sR}[0]{\mathbb{R}} \newcommand{\sC}[0]{\mathbb{C}} \newcommand{\sN}[0]{\mathbb{N}} \newcommand{\sZ}[0]{\mathbb{Z}}

\newcommand{\R}[0]{\mathbb{R}} \newcommand{\C}[0]{\mathbb{C}} \newcommand{\N}[0]{\mathbb{N}} \newcommand{\Z}[0]{\mathbb{Z}}

%\usepackage{bbm} %\newcommand{\N}{\mathbbmss{N}} %\newcommand{\Z}{\mathbbmss{Z}} %\newcommand{\C}{\mathbbmss{C}} %\newcommand{\R}{\mathbbmss{R}} %\newcommand{\Q}{\mathbbmss{Q}}

\newcommand*{\norm}[1]{\lVert #1 \rVert} \newcommand*{\abs}[1]{| #1 |}

\newcommand{\Map}[3]{#1:#2\to#3} \newcommand{\Emb}[3]{#1:#2\hookrightarrow#3} \newcommand{\Mor}[3]{#2\overset{#1}\to#3}

\newcommand{\Cat}[1]{\mathcal{#1}} \newcommand{\Kat}[1]{\mathbf{#1}} \newcommand{\Func}[3]{\Map{#1}{\Cat{#2}}{\Cat{#3}}} \newcommand{\Funk}[3]{\Map{#1}{\Kat{#2}}{\Kat{#3}}}

\newcommand{\intrv}[2]{\langle #1,#2 \rangle}

\newcommand{\vp}{\varphi} \newcommand{\ve}{\varepsilon}

\newcommand{\Invimg}[2]{\inv{#1}(#2)} \newcommand{\Img}[2]{#1[#2]} \newcommand{\ol}[1]{\overline{#1}} \newcommand{\ul}[1]{\underline{#1}} \newcommand{\inv}[1]{#1^{-1}} \newcommand{\limti}[1]{\lim\limits_{#1\to\infty}}

\newcommand{\Ra}{\Rightarrow}

%fonts \newcommand{\mc}{\mathcal}

%shortcuts \newcommand{\Ob}{\mathrm{Ob}} \newcommand{\Hom}{\mathrm{hom}} \newcommand{\homs}[2]{\mathrm{hom(}{#1},{#2}\mathrm )} \newcommand{\Eq}{\mathrm{Eq}} \newcommand{\Coeq}{\mathrm{Coeq}}

%theorems \newtheorem{THM}{Theorem} \newtheorem{DEF}{Definition} \newtheorem{PROP}{Proposition} \newtheorem{LM}{Lemma} \newtheorem{COR}{Corollary} \newtheorem{EXA}{Example}

%categories \newcommand{\Top}{\Kat{Top}} \newcommand{\Haus}{\Kat{Haus}} \newcommand{\Set}{\Kat{Set}}

%diagrams \newcommand{\UnimorCD}[6]{ \xymatrix{ {#1} \ar[r]^{#2} \ar[rd]_{#4}& {#3} \ar@{-->}[d]^{#5} \\ & {#6} } }

\newcommand{\RovnostrCD}[6]{ \xymatrix@C=10pt@R=17pt{ & {#1} \ar[ld]_{#2} \ar[rd]^{#3} \\ {#4} \ar[rr]_{#5} && {#6} } }

\newcommand{\RovnostrCDii}[6]{ \xymatrix@C=10pt@R=17pt{ {#1} \ar[rr]^{#2} \ar[rd]_{#4}&& {#3} \ar[ld]^{#5} \\ & {#6} } }

\newcommand{\RovnostrCDiiop}[6]{ \xymatrix@C=10pt@R=17pt{ {#1} && {#3} \ar[ll]_{#2} \\ & {#6} \ar[lu]^{#4} \ar[ru]_{#5} } }

\newcommand{\StvorecCD}[8]{ \xymatrix{ {#1} \ar[r]^{#2} \ar[d]_{#4} & {#3} \ar[d]^{#5} \\ {#6} \ar[r]_{#7} & {#8} } }

\newcommand{\TriangCD}[6]{ \xymatrix{ {#1} \ar[r]^{#2} \ar[rd]_{#4}& {#3} \ar[d]^{#5} \\ & {#6} } }

\begin{document}

\textbf{Definition 0.1}

A \htmladdnormallink{morphism}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} $\Map fAB$ is a \emph{monomorphism}, if for any two morphisms $\Map{g,h}CA$ the equality $f\circ g=f\circ h$ implies $h=g$.

\end{document}