You've pretty much got it. A monoid is a two argunent operation and a data type with 3 properties: It's 'chainable', or the more precise mathematical term is "

You've pretty much got it. A monoid is a two argunent operation and a data type with 3 properties: It's 'chainable', or the more precise mathematical term is "closed". It has a value that can be used as an identity. And it's associative. Where associative means that when 'chaining' multiple operations (as you termed it) it doesn't matter how you group with parentheses; it'll produce the same result.