Cartesian square

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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 , .


[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098