canonical

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

Examples

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

Notes

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

Title	canonical
Canonical name	Canonical
Date of creation	2013-03-22 14:44:32
Last modified on	2013-03-22 14:44:32
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	6
Author	mathcam (2727)
Entry type	Definition
Classification	msc 00A20
Related topic	CanonicalFormOfElementOfNumberField