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# 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 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.

2.

# Notes

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

# References

- 1 Wikipedia, article on canonical.

Related:

CanonicalFormOfElementOfNumberField

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

00A20*no label found*

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## Comments

## "canonical" for linear maps

A canonical linear map can be defined without choosing a basis.

Simple example, multiply every vector by some fixed scalar.