366 For convenience we assume that fields are enriched over Vect.

   366 For convenience we assume that fields are enriched over Vect.

   367 

   367 

   368 Local relations are subspaces $U(B; c)\sub \cC(B; c)$ of the fields on balls which form an ideal under gluing.

   368 Local relations are subspaces $U(B; c)\sub \cC(B; c)$ of the fields on balls which form an ideal under gluing.

   369 Again, we give the examples first.

   369 Again, we give the examples first.

   370 

   370 

   372 \begin{example}[contd.]

   372 \begin{example}[contd.]

   373 For maps into spaces, $U(B; c)$ is generated by fields of the form $a-b \in \lf(B; c)$,

   373 For maps into spaces, $U(B; c)$ is generated by fields of the form $a-b \in \lf(B; c)$,

   374 where $a$ and $b$ are maps (fields) which are homotopic rel boundary.

   374 where $a$ and $b$ are maps (fields) which are homotopic rel boundary.

   375 \end{example}

   375 \end{example}

   376 

   376 

   377 \begin{example}[contd.]

   377 \begin{example}[contd.]

   378 For $n$-category pictures, $U(B; c)$ is equal to the kernel of the evaluation map

   378 For $n$-category pictures, $U(B; c)$ is equal to the kernel of the evaluation map

   379 $\lf(B; c) \to \mor(c', c'')$, where $(c', c'')$ is some (any) division of $c$ into

   379 $\lf(B; c) \to \mor(c', c'')$, where $(c', c'')$ is some (any) division of $c$ into

   380 domain and range.

   380 domain and range.

   381 \end{example}

   381 \end{example}

   382 

   384 

   383 These motivate the following definition.

   385 These motivate the following definition.

   384 

   386 

   385 \begin{defn}

   387 \begin{defn}

   386 A {\it local relation} is a collection subspaces $U(B; c) \sub \lf(B; c)$,

   388 A {\it local relation} is a collection subspaces $U(B; c) \sub \lf(B; c)$,