monad

noun

Etymology: From Latin monas (“unit”) (from Ancient Greek μονάς (monás), from μόνος (mónos), from Proto-Indo-European *men-). By surface analysis, mono- + -ad.

1. One thing, one being, one item.
2. A group of entities or items treated as one entity.
3. An ultimate atom, or simple, unextended point; something ultimate and indivisible.

   “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.”

4. A single individual (such as a pollen grain) that is free from others, not united in a group.
5. A single-celled organism. (See Monas.)
6. A monoid object in the category of endofunctors of a fixed category.
7. A data type which represents a specific form of computation, along with the operations "return" and "bind".

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