canonical

A mathematical object is said to be canonical if it arises in a natural way without introducing any additional objects.

Examples

1. 1.

Suppose $A\times B$ is the Cartesian product of sets $A,B$. Then $A\times B$ has two $A\times B\to A$ 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.

2. 2.

http://planetmath.org/CanonicalProjectioncanonical projection (in group theory)

Notes

For a discussion of the theological use of canonical, see [1].

References

• 1 Wikipedia, article on http://en.wikipedia.org/wiki/Canonicalcanonical.
Title canonical Canonical 2013-03-22 14:44:32 2013-03-22 14:44:32 mathcam (2727) mathcam (2727) 6 mathcam (2727) Definition msc 00A20 CanonicalFormOfElementOfNumberField