You are using the exact reasoning I was talking about. Monoids are monoids. That is what they are. 99% of programmers are not familiar with them. If you call it "addable" or "joinable" or "appendable" then you are just making people think that one subset of some monoids is the definition of monoids when it isn't. They still don't know what monoids are, now they just also don't know what they are called. You are literally giving it an incorrect and misleading name. All that does is confuse people. You have to learn what monoids actually are even if you call them "addable"s. Rather than learning a misleading name for them, it is quite simple to learn a new term like "monoid". Considering there is really only 3 that people need to learn (monoid, functor, monad) this is not an overwhelming burden.