canonical
Canonical
2004-10-16 17:49:41
2004-10-17 04:57:12
Definition
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A mathematical object is said to be \emph{canonical}
if it arises in a natural way without introducing any additional objects.
\subsubsection*{Examples}
\begin{enumerate}
\item Suppose $A\times B$ is the Cartesian product of sets $A,B$.
Then $A\times B$ has two \PMlinkescapetext{canonical projections}
$A\times B\to A$
and $A\times B\to B$ defined in a natural way. Of course, if
we assume more structure of $A,B$ there are also other projections.
\item \PMlinkname{canonical projection}{CanonicalProjection} (in group theory)
\end{enumerate}
\subsubsection*{Notes}
For a discussion of the theological use of canonical, see \cite{wiki}.
\begin{thebibliography}{9}
\bibitem{wiki} Wikipedia, article on \PMlinkexternal{canonical}{http://en.wikipedia.org/wiki/Canonical}.
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