cartesian object

**2-category theory**
## Definitions
* 2-category
* strict 2-category
* bicategory
* enriched bicategory
## Transfors between 2-categories
* 2-functor
* pseudofunctor
* lax functor
* equivalence of 2-categories
* 2-natural transformation
* lax natural transformation
* icon
* modification
* Yoneda lemma for bicategories
## Morphisms in 2-categories
* fully faithful morphism
* faithful morphism
* conservative morphism
* pseudomonic morphism
* discrete morphism
* eso morphism
## Structures in 2-categories
* adjunction
* mate
* monad
* cartesian object
* fibration in a 2-category
* codiscrete cofibration
## Limits in 2-categories
* 2-limit
* 2-pullback
* comma object
* inserter
* inverter
* equifier
## Structures on 2-categories
* 2-monad
* lax-idempotent 2-monad
* pseudomonad
* pseudoalgebra for a 2-monad
* monoidal 2-category
* cartesian bicategory
* Gray tensor product
* proarrow equipment

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)