**Puzzle 102.** What is the category with the fewest morphisms that is not a preorder?

Dan Oneata gave a nice answer in comment #3: he chose the unique category with a single object, \\(\star\\), and two morphisms, \\(1_{\star}\\) and \\(f\\), such that \\(f \circ f = 1\_\star\\).

**Puzzle 102\\({}^\prime\\).** What's the usual name for this category?

Hint: a category with one object is the same as a [monoid](https://en.wikipedia.org/wiki/Monoid), and a monoid where every element has an inverse is called a [group](https://en.wikipedia.org/wiki/Group_(mathematics)).