Monad

A monad is a monoid in the category of endofunctors.

Gnosticism was a religious movement older than Christianity. There were both types of Christian and non-Christian Gnosticism because there was syncretism, or mixing. They believed that humans were trapped in their bodies and in this evil material world that was created by a cosmic disaster, by a malevolent deity who was not Christ. Christian Gnostics believed that Christ was one of the aeons or divine beings from the Pleroma, the Divine Realm, as described in the Apocryphon of John, part of the Nag Hammadi Library of Gnostic literature. Salvation was by esoteric knowledge, although ultimately self-knowledge. Gnostics believed in the dualism of the good spirit and evil matter. The material world was an evil place from where Gnostics had to escape. They believed that not all humans had the Divine Spark. The aeons emanated from the Ultimate God, the Monad in the Pleroma. The origins of Gnosticism are unclear today, but probably it came from Persia or further east. It had a lot of Greek influences. Today, after the discovery of the Nag Hammadi Library as leather-bound papyrus codices in a sealed jar in Egypt, in 1945, some people are trying to revive Gnosticism. "Gnōsis" is Greek for knowledge.

Hence Leibnitz, who looked upon things as noumena, after denying them everything like external relation, and therefore also composition or combination, declared that all substances, even the component parts of matter, were simple substances with powers of representation, in one word, monads.

“If we are to embark upon speculation”, said Goethe, continuing his discourse, “then I really do not see why the monad to which we owe Wieland's appearance on our planet should be unable in its new condition to enter into the highest combinations that are possible in this universe.

Pythagoras considered numbers as the essence and principle of all things, and attributed to them a real and distinct existence; so that, in his view, they were the elements out of which the universe was constructed. […] The "Monad" or unit he regarded as the source of all numbers.

More than thirty years ago two atoms of the eternal Energy sped forth from the heart of it which we call God[…]. Perhaps these two atoms, or essences, or monads indestructible, did but repeat an adventure, or many, many adventures.

The properties that make the Maybe type a monad are its type constructor Maybe a, our chaining function (>>?), and the injector function Just.