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].
References
 1 Wikipedia, article on http://en.wikipedia.org/wiki/Canonicalcanonical.
Title  canonical 

Canonical name  Canonical 
Date of creation  20130322 14:44:32 
Last modified on  20130322 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 