Contents

# Contents

## Idea

In the context of 2-category theory, a cartesian closed 2-category is a 2-category, $\mathcal{B}$, with finite products and a cartesian closed structure. For any $A$, $B$ in $\mathcal{B}$, there is an exponential object $B^A$, an evaluation 1-arrow, $eval_{A, B}: B^A \times A \to B$, and for every $X$ an adjoint equivalence between $\mathcal{B}(X, B^A)$ and $\mathcal{B}(X \times A, B)$.

The concept was introduced in (Makkai 96). There is no connection to the concept of cartesian bicategory.

## Examples

• the 2-category of generalized species (FGHW).

• the 2-category of cartesian distributors.