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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 |