Definition:Underlying Set Functor

Definition
Let $\mathbf{Set}$ be the category of sets.

Let $\mathbf C$ be a metacategory with:


 * A collection of sets as objects;
 * A collection of mappings as morphisms.

The underlying set functor $\left\vert{\cdot}\right\vert: \mathbf C \to \mathbf{Set}$ is defined in the following cases.