Cat - Category of Small Categories
Table of Contents
1. Definition
The category Cat of Small Categories has as its:
- Objects
- All small categories
- Morphisms
- All functors between small categories
Some authors also want to discuss the category of all categories
2. Properties
2.1. Cartesian Closed
The category Cat is Cartesian closed, i.e., the exponential objects of Cat are functor categories.
(See Mac Lane, Categories for the Working Mathematician, 2nd ed, Chapter IV, section 6, penultimate paragraph.)
3. References
- Saunders Mac Lane, Categories for the Working Mathematician. 2nd ed, Springer.