 Category of small categories

Objects are small categories and morphisms are functors. Its products pair objects and arrows componentwise. Its exponential objects are functor categories, as shown by the currying adjunction for small categories.

The **category of small categories**, often denoted as **Cat**, is a mathematical category in category theory where the objects are small categories (categories that have a hom-set for every pair of objects that is a set, not a proper class) and the morphisms are functors between these categories. ### Key Elements: 1. **Objects**: The objects of **Cat** are **small categories**.