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49 Fields on $n$-manifolds will be enriched over $\cS$. |
49 Fields on $n$-manifolds will be enriched over $\cS$. |
50 Good examples to keep in mind are $\cS = \Set$ or $\cS = \Vect$. |
50 Good examples to keep in mind are $\cS = \Set$ or $\cS = \Vect$. |
51 The presentation here requires that the objects of $\cS$ have an underlying set, |
51 The presentation here requires that the objects of $\cS$ have an underlying set, |
52 but this could probably be avoided if desired. |
52 but this could probably be avoided if desired. |
53 |
53 |
54 A $n$-dimensional {\it system of fields} in $\cS$ |
54 An $n$-dimensional {\it system of fields} in $\cS$ |
55 is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$ |
55 is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$ |
56 together with some additional data and satisfying some additional conditions, all specified below. |
56 together with some additional data and satisfying some additional conditions, all specified below. |
57 |
57 |
58 Before finishing the definition of fields, we give two motivating examples of systems of fields. |
58 Before finishing the definition of fields, we give two motivating examples of systems of fields. |
59 |
59 |