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kompik

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thales.doa.fmph.uniba.sk/sleziak
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% this is the default PlanetMath 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} \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} } }
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