# nLab cartesian object

A cartesian object in a 2-category with finite limits is an object $A$ such that the diagonal morphism $A\to A\times A$ and the unique map $A\to 1$ have right adjoints. Any cartesian object is automatically a pseudomonoid in a canonical way.

For example, a cartesian object in Cat is precisely a category with finite products, which is of course a monoidal category in a canonical way.

Revised on May 21, 2010 19:15:48 by Mike Shulman (128.192.37.11)