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docs/src/man/multifusioncats.md

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@@ -110,7 +110,7 @@ $$\mathcal{C}_{ij} \times \mathcal{C}_{ji} \rightarrow \mathcal{C}_i,$$
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just like what we concluded when considering opposite module categories outside of the multifusion structure.
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### 2-category and coloring
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Multifusion categories can also be interpreted as 2-categories. We still interpret the objects of this 2-category the same way. The 1-morphisms are the subcategories themselves, and the 2-morphisms the morphisms of the multifusion category. The graphical calculus of monoidal 1-categories can be extended to 2-categories by use of *colorings*. We have previously differed between module strands and fusion strands by the color of the strand itself. However, in 2-categories the strands (1-morphisms) separate regions which are colored based on the objects they are representing. Since we draw the strands vertically, a single strand results in a left and right region, and the colorings will determine the fusion category which fuses from the left or right with that single strand. In particular, fusion strands necessarily have the same coloring on the left and right, while module strands have a mismatching coloring.
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Multifusion categories can also be interpreted as 2-categories. We still interpret the objects of this 2-category the same way. The 1-morphisms are the subcategories themselves, and the 2-morphisms the morphisms of the multifusion category. The graphical calculus of monoidal 1-categories can be extended to 2-categories by use of *colorings* [henriques2020](@cite). We have previously differed between module strands and fusion strands by the color of the strand itself. However, in 2-categories the strands (1-morphisms) separate regions which are colored based on the objects they are representing. Since we draw the strands vertically, a single strand results in a left and right region, and the colorings will determine the fusion category which fuses from the left or right with that single strand. In particular, fusion strands necessarily have the same coloring on the left and right, while module strands have a mismatching coloring.
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The simplest non-trivial fusion diagram is a trivalent junction:
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