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1 %!TEX root = ../blob1.tex |
1 %!TEX root = ../blob1.tex |
2 |
2 |
3 \section{Definitions} |
3 \section{Definitions} |
4 \label{sec:definitions} |
4 \label{sec:definitions} |
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5 |
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6 \nn{this section is a bit out of date; needs to be updated |
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7 to fit with $n$-category definition given later} |
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8 |
6 \subsection{Systems of fields} |
9 \subsection{Systems of fields} |
7 \label{sec:fields} |
10 \label{sec:fields} |
8 |
11 |
9 Let $\cM_k$ denote the category (groupoid, in fact) with objects |
12 Let $\cM_k$ denote the category (groupoid, in fact) with objects |
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20 |
18 A $n$-dimensional {\it system of fields} in $\cS$ |
21 A $n$-dimensional {\it system of fields} in $\cS$ |
19 is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$ |
22 is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$ |
20 together with some additional data and satisfying some additional conditions, all specified below. |
23 together with some additional data and satisfying some additional conditions, all specified below. |
21 |
24 |
22 \nn{refer somewhere to my TQFT notes \cite{kw:tqft}, and possibly also to paper with Chris} |
25 \nn{refer somewhere to my TQFT notes \cite{kw:tqft}} |
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24 Before finishing the definition of fields, we give two motivating examples |
27 Before finishing the definition of fields, we give two motivating examples |
25 (actually, families of examples) of systems of fields. |
28 (actually, families of examples) of systems of fields. |
26 |
29 |
27 The first examples: Fix a target space $B$, and let $\cC(X)$ be the set of continuous maps |
30 The first examples: Fix a target space $B$, and let $\cC(X)$ be the set of continuous maps |