4 |
4 |
5 \usepackage{amsmath,amssymb,amsfonts,amsthm} |
5 \usepackage{amsmath,amssymb,amsfonts,amsthm} |
6 \usepackage{ifpdf} |
6 \usepackage{ifpdf} |
7 |
7 |
8 \usepackage[all,color]{xy} |
8 \usepackage[all,color]{xy} |
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9 \SelectTips{cm}{} |
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10 % This may speed up compilation of complex documents with many xymatrices. |
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11 %\CompileMatrices |
9 |
12 |
10 \usepackage[section]{placeins} |
13 \usepackage[section]{placeins} |
11 \usepackage{leftidx} |
14 \usepackage{leftidx} |
12 \usepackage{stmaryrd} % additional math symbols, e.g. \mapsfrom |
15 \usepackage{stmaryrd} % additional math symbols, e.g. \mapsfrom |
13 \usepackage{microtype} |
16 \usepackage{microtype} |
14 |
17 |
15 \SelectTips{cm}{} |
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16 % This may speed up compilation of complex documents with many xymatrices. |
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17 %\CompileMatrices |
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18 |
18 |
19 % ---------------------------------------------------------------- |
19 % ---------------------------------------------------------------- |
20 \vfuzz2pt % Don't report over-full v-boxes if over-edge is small |
20 \vfuzz2pt % Don't report over-full v-boxes if over-edge is small |
21 \hfuzz2pt % Don't report over-full h-boxes if over-edge is small |
21 \hfuzz2pt % Don't report over-full h-boxes if over-edge is small |
22 % ---------------------------------------------------------------- |
22 % ---------------------------------------------------------------- |
52 \newtheorem{prop}{Proposition}[subsection] |
52 \newtheorem{prop}{Proposition}[subsection] |
53 \newtheorem{conj}[prop]{Conjecture} |
53 \newtheorem{conj}[prop]{Conjecture} |
54 \newtheorem{thm}[prop]{Theorem} |
54 \newtheorem{thm}[prop]{Theorem} |
55 \newtheorem{lem}[prop]{Lemma} |
55 \newtheorem{lem}[prop]{Lemma} |
56 \newtheorem*{lem*}{Lemma} |
56 \newtheorem*{lem*}{Lemma} |
57 \newtheorem{claim}[prop]{Claim} |
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58 \newtheorem{cor}[prop]{Corollary} |
57 \newtheorem{cor}[prop]{Corollary} |
59 \newtheorem*{cor*}{Corollary} |
58 \newtheorem*{cor*}{Corollary} |
60 \newtheorem*{exc}{Exercise} |
59 \newtheorem*{exc}{Exercise} |
61 \newtheorem{defn}[prop]{Definition} % numbered definition |
60 \newtheorem{defn}[prop]{Definition} % numbered definition |
62 \newtheorem*{defn*}{Definition} % unnumbered definition |
61 \newtheorem*{defn*}{Definition} % unnumbered definition |
64 \newtheorem{property}[prop]{Property} |
63 \newtheorem{property}[prop]{Property} |
65 \newtheorem{axiom}[prop]{Axiom} |
64 \newtheorem{axiom}[prop]{Axiom} |
66 \newtheorem{module-axiom}[prop]{Module Axiom} |
65 \newtheorem{module-axiom}[prop]{Module Axiom} |
67 \newenvironment{rem}{\noindent\textsl{Remark.}}{} % perhaps looks better than rem above? |
66 \newenvironment{rem}{\noindent\textsl{Remark.}}{} % perhaps looks better than rem above? |
68 \newtheorem{rem*}[prop]{Remark} |
67 \newtheorem{rem*}[prop]{Remark} |
69 \newtheorem{remark}[prop]{Remark} |
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70 \numberwithin{equation}{section} |
68 \numberwithin{equation}{section} |
71 %% example is defined in article_preamble.tex, for compatibility with beamer. |
69 %% example, claim and remark are defined in article_preamble.tex, for compatibility with beamer and PNAS |
72 |
70 |
73 |
71 |
74 % Marginal notes in draft mode ----------------------------------- |
72 % Marginal notes in draft mode ----------------------------------- |
75 \newcommand{\scott}[1]{\stepcounter{comment}{{\color{blue} $\star^{(\arabic{comment})}$}}\marginpar{\color{blue} $\star^{(\arabic{comment})}$ \usefont{T1}{scott}{m}{n} #1 --S}} % draft mode |
73 \newcommand{\scott}[1]{\stepcounter{comment}{{\color{blue} $\star^{(\arabic{comment})}$}}\marginpar{\color{blue} $\star^{(\arabic{comment})}$ \usefont{T1}{scott}{m}{n} #1 --S}} % draft mode |
76 \newcommand{\kevin}[1]{\stepcounter{comment}{\color[rgb]{.2,.5,.6} $\star^{(\arabic{comment})}$}\marginpar{\color{green} $\star^{(\arabic{comment})}$ #1 --K}} % draft mode |
74 \newcommand{\kevin}[1]{\stepcounter{comment}{\color[rgb]{.2,.5,.6} $\star^{(\arabic{comment})}$}\marginpar{\color{green} $\star^{(\arabic{comment})}$ #1 --K}} % draft mode |
115 \newcommand{\HC}{\operatorname{Hoch}} |
113 \newcommand{\HC}{\operatorname{Hoch}} |
116 \newcommand{\HH}{\operatorname{HH}} |
114 \newcommand{\HH}{\operatorname{HH}} |
117 |
115 |
118 \newcommand{\cell}{\mathfrak{D}} |
116 \newcommand{\cell}{\mathfrak{D}} |
119 |
117 |
120 \newcommand{\selfarrow}{\ensuremath{\!\!\!\!\!\!\xymatrix{ \ar@(ru,rd)@<-1ex>[]}\phantom{++.\!\!}}} |
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121 \newsavebox{\selfarrowcontents} |
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122 \savebox{\selfarrowcontents}{\selfarrow} |
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123 \renewcommand{\selfarrow}{\usebox{\selfarrowcontents}} |
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124 |
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125 |
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126 \def\bc{{\mathcal B}} |
118 \def\bc{{\mathcal B}} |
127 \def\btc{{\mathcal{BT}}} |
119 \def\btc{{\mathcal{BT}}} |
128 |
120 |
129 \newcommand{\into}{\hookrightarrow} |
121 \newcommand{\into}{\hookrightarrow} |
130 \newcommand{\onto}{\twoheadrightarrow} |
122 \newcommand{\onto}{\twoheadrightarrow} |
155 |
147 |
156 \newcommand{\bdy}{\partial} |
148 \newcommand{\bdy}{\partial} |
157 \newcommand{\compose}{\circ} |
149 \newcommand{\compose}{\circ} |
158 \newcommand{\eset}{\emptyset} |
150 \newcommand{\eset}{\emptyset} |
159 |
151 |
160 \newcommand{\Set}{\text{\textbf{Set}}} |
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161 \newcommand{\Vect}{\text{\textbf{Vect}}} |
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162 \newcommand{\Kom}{\text{\textbf{Kom}}} |
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163 \newcommand{\Cat}{\mathcal{C}} |
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164 |
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165 \newcommand{\psmallmatrix}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} |
152 \newcommand{\psmallmatrix}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} |
166 |
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167 \newcommand{\qiq}[2]{[#1]_{#2}} |
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168 \newcommand{\qi}[1]{\qiq{#1}{q}} |
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169 \newcommand{\qdim}{\operatorname{dim_q}} |
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170 |
153 |
171 \newcommand{\directSum}{\oplus} |
154 \newcommand{\directSum}{\oplus} |
172 \newcommand{\DirectSum}{\bigoplus} |
155 \newcommand{\DirectSum}{\bigoplus} |
173 \newcommand{\tensor}{\otimes} |
156 \newcommand{\tensor}{\otimes} |
174 \newcommand{\Tensor}{\bigotimes} |
157 \newcommand{\Tensor}{\bigotimes} |
175 |
158 |
176 \newcommand{\db}[1]{\left(\left(#1\right)\right)} |
159 %\newcommand{\selfarrow}{\ensuremath{\!\!\!\!\!\!\xymatrix{ \ar@(ru,rd)@<-1ex>[]}\phantom{++.\!\!}}} |
177 |
160 %\newsavebox{\selfarrowcontents} |
178 \newcommand{\Mat}[1]{\mathbf{Mat}\left(#1\right)} |
161 %\savebox{\selfarrowcontents}{\selfarrow} |
179 \newcommand{\Inv}[1]{\operatorname{Inv}\left(#1\right)} |
162 %\renewcommand{\selfarrow}{\usebox{\selfarrowcontents}} |
180 \newcommand{\Hom}[3]{\operatorname{Hom}_{#1}\left(#2,#3\right)} |
163 \newcommand{\selfarrow}{\ensuremath{\smash{\tikz[baseline]{\draw[->] (0,0.2) .. controls (0.6,0.8) and (0.6,-0.6) .. (0,0);}}}} |
181 \newcommand{\End}[1]{\operatorname{End}\left(#1\right)} |
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182 \newcommand{\Obj}{\operatorname{Obj}} |
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183 |
164 |
184 \newcommand{\CM}[2]{C_*(\Maps(#1 \to #2))} |
165 \newcommand{\CM}[2]{C_*(\Maps(#1 \to #2))} |
185 \newcommand{\CD}[1]{C_*(\Diff(#1))} |
166 \newcommand{\CD}[1]{C_*(\Diff(#1))} |
186 \newcommand{\CH}[1]{C_*(\Homeo(#1))} |
167 \newcommand{\CH}[1]{C_*(\Homeo(#1))} |
187 |
168 |
188 \newcommand{\cl}[1]{\underrightarrow{#1}} |
169 \newcommand{\cl}[1]{\underrightarrow{#1}} |
189 |
170 |
190 \newcommand{\directSumStack}[2]{{\begin{matrix}#1 \\ \DirectSum \\#2\end{matrix}}} |
171 \newcommand{\Set}{\text{\textbf{Set}}} |
191 \newcommand{\directSumStackThree}[3]{{\begin{matrix}#1 \\ \DirectSum \\#2 \\ \DirectSum \\#3\end{matrix}}} |
172 \newcommand{\Vect}{\text{\textbf{Vect}}} |
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173 \newcommand{\Kom}{\text{\textbf{Kom}}} |
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174 \newcommand{\Cat}{\mathcal{C}} |
192 |
175 |
193 \newcommand{\grading}[1]{{\color{blue}\{#1\}}} |
176 \newcommand{\Inv}[1]{\operatorname{Inv}\left(#1\right)} |
194 \newcommand{\shift}[1]{\left[#1\right]} |
177 \newcommand{\Hom}[3]{\operatorname{Hom}_{#1}\left(#2,#3\right)} |
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178 \newcommand{\End}[1]{\operatorname{End}\left(#1\right)} |
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179 \newcommand{\Obj}{\operatorname{Obj}} |
195 |
180 |
196 \newenvironment{narrow}[2]{% |
181 \newenvironment{narrow}[2]{% |
197 \vspace{-0.4cm}% horrible hack, by scott % this only seems to be appropriate in beamer mode... |
182 \vspace{-0.4cm}% horrible hack, by scott % this only seems to be appropriate in beamer mode... |
198 \begin{list}{}{% |
183 \begin{list}{}{% |
199 \setlength{\topsep}{0pt}% |
184 \setlength{\topsep}{0pt}% |