cartesian object

A **cartesian object** in a 2-category with finite products 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.

Last revised on December 29, 2017 at 21:39:17. See the history of this page for a list of all contributions to it.