Name of a groupoid

Question

Let $S$ be an arbitrary set. Consider the category

• whose objects are the points of $S$;
• whose morphisms are the pairs $(a,b) \in S^2$, with starting and ending objects respectively $a$ and $b$;
• such that, for all $(a,b),(b,c) \in S^2$, $(a,b) \circ (b,c):=(a,c)$.

It is clear that this category is a groupoid.

Question: Does this groupoid have a name in the literature?

Answer 1

This is called the indiscrete or codiscrete groupoid, by analogy with the indiscrete topology.