We previously looked at a generalization of the familiar algebraic concept of a monoid to a category. We’re now in a position to give the “mathematician’s definition” of a monad. People seem to have different opinions of this definition. I personally think that it’s simple, elegant, and captures the spirit of generality of category theory. I have heard that some people use this definition to belittle or confuse people. Perhaps it’s just that people feel belittled or confused by it. In any case, describing a monad isn’t easy, and we shouldn’t feel bad if we don’t understand it very well at first.