# Cartesian square

From Encyclopedia of Mathematics

*co-universal square, pull-back square, in a category*

The diagram

Here (the notation is also used) is the fibred product of the objects and , which is associated with

and and are the canonical projections. The diagram

is a Cartesian square if and only if it is commutative and if for any pair of morphisms , such that there exists a unique morphism which satisfies the conditions , .

#### References

[1] | I. Bucur, A. Deleanu, "Introduction to the theory of categories and functors" , Wiley (1968) |

**How to Cite This Entry:**

Cartesian square. O.A. Ivanova (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Cartesian_square&oldid=13918

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098