File:CategoryBraiding-03.png

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Commuative diagram defining a braided monoidal category.

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\begin{diagram}[vtrianglewidth=2.1em,tight]
& & (A\otimes B)\otimes C & & \rTo^{\scriptstyle\gamma} & & C\otimes(A\otimes B) \\
& \ruTo^{\scriptstyle\alpha^{-1}} & & & & & & \rdTo>{\scriptstyle\alpha^{-1}} \\
A\otimes (B\otimes C) & & & & & & & & (C\otimes A)\otimes B \\
& \rdTo<{\scriptstyle 1\otimes\gamma} & & & & & & \ruTo>{\scriptstyle\gamma\otimes 1} \\
& & A\otimes (C\otimes B) & & \rTo_{\scriptstyle\alpha^{-1}} & & (A\otimes C)\otimes B \\
\end{diagram}