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\nn{This file is obsolete.}
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\todo{beginning of scott's attempt to write down what fields are...}
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\newcommand{\manifolds}[1]{\cM_{#1}}
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\newcommand{\closedManifolds}[1]{\cM_{#1}^{\text{closed}}}
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\newcommand{\boundaryConditions}[1]{\cM_{#1}^{\bdy}}
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Let $\manifolds{k}$ be the groupoid of manifolds (possibly with boundary) of dimension $k$ and diffeomorphisms between them. Write
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$\closedManifolds{k}$ for the subgroupoid of closed manifolds. Taking the boundary gives a functor $\bdy : \manifolds{k} \to \closedManifolds{k-1}$.
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Both $\manifolds{k}$ and $\closedManifolds{k}$ are symmetric tensor categories under the operation of disjoint union.
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\begin{defn}
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A \emph{system of fields} is a collection of functors $\cF_k$ associating a `set of fields' to each manifold of dimension at most $n$.
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