3 ms·

That's absolutely fine. Then you also have to mention that there's an identity element. Once you've used the words "associatively" and "identity" it's no long

• romwell 9y ago
  Well, you still have to use the words "associativity" and "identity" when you describe the operation and say what the identity element is. You can't just say that you can "combine" elements "monoidally" for it to mean anything. Also, the elements are still combined associatively. With closure and and identity properties, the set forms a monoid under this operation. "Monoidness" is not a property of operation (in a way that the language is usually used, at least in math). For that matter, "combine monoidally" is a phrase that has 2 Google hits at the moment, which indicates to me that in real life, you still have to resort to less-shiny words to describe things.
  • tome 9y ago
    > You can't just say that you can "combine" elements "monoidally" for it to mean anything. ... For that matter, "combine monoidally" is a phrase that has 2 Google hits at the moment, which indicates to me that in real life, you still have to resort to less-shiny words to describe things. There doesn't seems anything hugely objectionable to me in saying "Bars combine monoidally". But if you prefer, one can say "Bar forms a monoid under baz and quux". It may not be obvious to you that it increases simplicity merely to combine two words into one but across an ecosystem of perhaps a thousand Monoid instances it indeed is.