Simplex category

In mathematics, particularly in category theory, a **simplex category** is a category that arises from the study of simplices, which are generalizations of the concept of a triangle to arbitrary dimensions. A simplex can be thought of as a geometric object corresponding to the set of all convex combinations of a finite set of points. The **n-simplex** is defined as the convex hull of its \((n+1)\) vertices in \((n+1)\)-dimensional space.