92 |
92 |
93 \begin{figure}[!ht] |
93 \begin{figure}[!ht] |
94 {\center |
94 {\center |
95 \beginpgfgraphicnamed{gadgets-external}% |
95 \beginpgfgraphicnamed{gadgets-external}% |
96 \begin{tikzpicture}[align=center,line width = 1.5pt] |
96 \begin{tikzpicture}[align=center,line width = 1.5pt] |
97 \newcommand{\xa}{2} |
97 \newcommand{\xxa}{2} |
98 \newcommand{\xb}{8} |
98 \newcommand{\xxb}{8} |
99 \newcommand{\ya}{14} |
99 \newcommand{\yya}{14} |
100 \newcommand{\yb}{10} |
100 \newcommand{\yyb}{10} |
101 \newcommand{\yc}{6} |
101 \newcommand{\yyc}{6} |
102 |
102 |
103 \node[box] at (-4,\yb) (tC) {$C$ \\ a `traditional' \\ weak $n$-category}; |
103 \node[box] at (-4,\yyb) (tC) {$C$ \\ a `traditional' \\ weak $n$-category}; |
104 \node[box] at (\xa,\ya) (C) {$\cC$ \\ a topological \\ $n$-category}; |
104 \node[box] at (\xxa,\yya) (C) {$\cC$ \\ a topological \\ $n$-category}; |
105 \node[box] at (\xb,\ya) (A) {$\underrightarrow{\cC}(M)$ \\ the (dual) TQFT \\ Hilbert space}; |
105 \node[box] at (\xxb,\yya) (A) {$\underrightarrow{\cC}(M)$ \\ the (dual) TQFT \\ Hilbert space}; |
106 \node[box] at (\xa,\yb) (FU) {$(\cF, U)$ \\ fields and\\ local relations}; |
106 \node[box] at (\xxa,\yyb) (FU) {$(\cF, U)$ \\ fields and\\ local relations}; |
107 \node[box] at (\xb,\yb) (BC) {$\bc_*(M; \cF)$ \\ the blob complex}; |
107 \node[box] at (\xxb,\yyb) (BC) {$\bc_*(M; \cF)$ \\ the blob complex}; |
108 \node[box] at (\xa,\yc) (Cs) {$\cC_*$ \\ an $A_\infty$ \\$n$-category}; |
108 \node[box] at (\xxa,\yyc) (Cs) {$\cC_*$ \\ an $A_\infty$ \\$n$-category}; |
109 \node[box] at (\xb,\yc) (BCs) {$\underrightarrow{\cC_*}(M)$}; |
109 \node[box] at (\xxb,\yyc) (BCs) {$\underrightarrow{\cC_*}(M)$}; |
110 |
110 |
111 |
111 |
112 |
112 |
113 \draw[->] (C) -- node[above] {$\displaystyle \colim_{\cell(M)} \cC$} node[below] {\S\S \ref{sec:constructing-a-tqft} \& \ref{ss:ncat_fields}} (A); |
113 \draw[->] (C) -- node[above] {$\displaystyle \colim_{\cell(M)} \cC$} node[below] {\S\S \ref{sec:constructing-a-tqft} \& \ref{ss:ncat_fields}} (A); |
114 \draw[->] (FU) -- node[below] {blob complex \\ for $M$} (BC); |
114 \draw[->] (FU) -- node[below] {blob complex \\ for $M$} (BC); |