I wonder what's the point of using such a phrase, it doesn't help you to grok the concept of monad. It can help you to know that someone has given a new definit

I wonder what's the point of using such a phrase, it doesn't help you to grok the concept of monad. It can help you to know that someone has given a new definition to sound cute, shame on them. By the way I admire MacLane as a math person, but people seem to use category theory to sell snake oil. Category theory is a tool to give names to some diagrams and properties that are used frequently to avoid repeating the same argument in proofs, is a dry (don't repeat yourself, as in the ruby motto). If you are an expert in category theory you can give short proofs of known facts. Category theory is like pipes in unix, you pipe diagrams to show properties. Grep, sed, awk analoges are functors, categories and natural transformations. The input is a collection of diagrams and the output is a new diagram that has a universal property and it receives a name and a collection of properties that are supposed to be useful to proof new theorems.