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659 \caption{Part of the proof that the four different horizontal compositions of 2-morphisms are equal.} |
659 \caption{Part of the proof that the four different horizontal compositions of 2-morphisms are equal.} |
660 \label{fig:horizontal-compositions-equal} |
660 \label{fig:horizontal-compositions-equal} |
661 \end{figure} |
661 \end{figure} |
662 |
662 |
663 Given 1-morphisms $a$, $b$ and $c$ of $D$, we define the associator from $(a\bullet b)\bullet c$ to $a\bullet(b\bullet c)$ |
663 Given 1-morphisms $a$, $b$ and $c$ of $D$, we define the associator from $(a\bullet b)\bullet c$ to $a\bullet(b\bullet c)$ |
664 as in Figure \nn{like triangle 4.a, but more general; use three colors as in that fig}. |
664 as in Figure \ref{fig:associator}. |
665 This is just a reparameterization of the pinched product $(a\bullet b\bullet c)\times I$ of $\cC$. |
665 This is just a reparameterization of the pinched product $(a\bullet b\bullet c)\times I$ of $\cC$. |
666 \begin{figure}[t] |
666 \begin{figure}[t] |
667 $$ |
667 $$ |
668 \mathfig{0.4}{triangle/triangle4a} |
668 \mathfig{0.4}{triangle/triangle4a} |
669 $$ |
669 $$ |