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return to viewing 'superdiagrams as heterofunctors'
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2008-09-18 21:25:59
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bci1
| \emph{Superdiagrams} $\Sigma_S$ are defined as heterofunctors $\F_S$ |
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2008-09-18 21:21:43
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bci1
The heterofunctors corresponding to
superdiagrams also need not be invertible (as in the case of \emph{supergroupoid} structures). |
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2008-08-28 00:12:14
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bci1
\begin{equation}
${\F_S} * {\F_C} := \F_S (\F_C)$,
\end{equation}
to be interpreted on the right hand side of the equarion as the heterofunctor acting on the
homofunctor(s) $F_C$ determined by the categorical diagram, or categorical sequence, $\Sigma_C$. |
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2008-08-27 20:39:17
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bci1
\textbf{Remark}
In a certain sense, the superdiagrams defined as superfunctors resemble also
the groupoid functor categories, and also with topological categories when one regards the
class of links between the different types of categorical diagrams as a meta-network or
\emph{metagraph} (in the sense defined by Saunders Mac Lane). |
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2008-08-27 20:31:04
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bci1
are;
one replaces the linked groups by categorical diagrams linked by hetero-fucntors between categorical diagrams or categorical sequences with different structure; such heterofunctors of diagrams also need not be invertible (as in the case of \emph{supergroupoid} structures).
\end{definition}
$\Sigma_C$ |
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