canonical

A mathematical object is said to be canonicalif 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, ifwe 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].