1582 

  1582 

  1583 %\nn{need to finish explaining why we have a system of fields;

  1583 %\nn{need to finish explaining why we have a system of fields;

  1584 %define $k$-cat $\cC(\cdot\times W)$}

  1584 %define $k$-cat $\cC(\cdot\times W)$}

  1585 

  1585 

  1586 \subsection{Modules}

  1586 \subsection{Modules}

  1588 Next we define ordinary and $A_\infty$ disk-like $n$-category modules.

  1588 Next we define ordinary and $A_\infty$ disk-like $n$-category modules.

  1589 The definition will be very similar to that of disk-like $n$-categories,

  1589 The definition will be very similar to that of disk-like $n$-categories,

  1590 but with $k$-balls replaced by {\it marked $k$-balls,} defined below.

  1590 but with $k$-balls replaced by {\it marked $k$-balls,} defined below.

  1591 

  1591 

  1592 Our motivating example comes from an $(m{-}n{+}1)$-dimensional manifold $W$ with boundary

  1592 Our motivating example comes from an $(m{-}n{+}1)$-dimensional manifold $W$ with boundary