There's an old mathematical wive's tale about the professor who, on the beginning of the first day of an abstract algebra course, writes the following definitio

There's an old mathematical wive's tale about the professor who, on the beginning of the first day of an abstract algebra course, writes the following definition down on the board: Definition: A group is a category with a single object, all of whose morphisms are both epic[1] and monic[2]. In particular, if you drop the epic and monic requirements, a category that has only one object can be viewed as a monoid[3] under morphism composition. [1]: http://en.wikipedia.org/wiki/Epimorphism http://en.wikipedia.org/wiki/Epimorphism [2]: http://en.wikipedia.org/wiki/Monomorphism http://en.wikipedia.org/wiki/Monomorphism [3]: http://en.wikipedia.org/wiki/Monoid http://en.wikipedia.org/wiki/Monoid