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**.
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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.