# Functor

If **A** and **B** are categories, then a **functor** *F* **from A to B** is a function that assigns

- to each
**A**-object*A*a**B**-object*F(A)*, and - to each
**A**-morphism*f: A → A'*a**B**-morphism*F(f): F(A) → F(A')*.

If **A** and **B** are categories, then a **functor** *F* **from A to B** is a function that assigns

- to each
**A**-object*A*a**B**-object*F(A)*, and - to each
**A**-morphism*f: A → A'*a**B**-morphism*F(f): F(A) → F(A')*.