Category, Functor, Monad, Comonad, etc. should mention algebraic laws

[Corbin Simpson]

For example, the algebraic laws for categories say that, for any arrow f. f;id == id;f == f. These laws are essential for functors and monads.

[Nikola Pavlovic]

I consider myself somewhat literate when it comes to functional programming (it was love at first sight), so naturally (or not?), I went straight down to the monad definition, kind of hoping for a mind-blowingly simple (possibly wrong, but practical) description. Next I went to Issues to create one showing my disappointment but thinking I ought to keep it constructive. Imagine my dismay and complacency when I realized somebody has already done it. Moreover, yours have been (from what I saw), solely constructive.
tldr. It's not an overstatement if I say I do not understand the aforementioned definitions.