text/ncat.tex
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  2128 When $n=1$ this is closely related to familiar $2$-categories consisting of 
  2128 When $n=1$ this is closely related to familiar $2$-categories consisting of 
  2129 algebras, bimodules and intertwiners (or a subcategory of that).
  2129 algebras, bimodules and intertwiners (or a subcategory of that).
  2130 The sphere module $n{+}1$-category is a natural generalization of the 
  2130 The sphere module $n{+}1$-category is a natural generalization of the 
  2131 algebra-bimodule-intertwiner 2-category to higher dimensions.
  2131 algebra-bimodule-intertwiner 2-category to higher dimensions.
  2132 
  2132 
  2133 Another possible name for this $n{+}1$-category is $n{+}1$-category of defects.
  2133 Another possible name for this $n{+}1$-category is the $n{+}1$-category of defects.
  2134 The $n$-categories are thought of as representing field theories, and the 
  2134 The $n$-categories are thought of as representing field theories, and the 
  2135 $0$-sphere modules are codimension 1 defects between adjacent theories.
  2135 $0$-sphere modules are codimension 1 defects between adjacent theories.
  2136 In general, $m$-sphere modules are codimension $m{+}1$ defects;
  2136 In general, $m$-sphere modules are codimension $m{+}1$ defects;
  2137 the link of such a defect is an $m$-sphere decorated with defects of smaller codimension.
  2137 the link of such a defect is an $m$-sphere decorated with defects of smaller codimension.
  2138 
  2138