For things like this I recommend going to wikipedia and looking up "Functor" -- there's some weird dislike of category theory terms but we're all fine with terms like "singleton" or "Factory"

You'll see the definition and be like, "shit that's just a map." We sell each other a bit short.

Likewise for applicative, monoid, monad -- they're mathematically pretty clear and if you squint while assuming a list is a category, you can probably read most of the definitions and get it.

functor -> equivalent of map for lists

monoid -> equivalent of having an identity ([]) and a join (a.concat) for lists

applicative -> equivalent of turning one element into a list

monad -> equivalent of unwrappering list items, applying a function to each, and rewrapping it

This is just for lists, but the terms are more powerful than that and have many variations. The nice thing is because it's universal. You don't have to wonder, "have I done this pattern right," because you test the laws for them. It might also help, for some of the laws, to remember identity and associativity as like from multiplication -- ie 1 * 9 = 9, 3 * 2 = 2 * 3