monad (disambiguation)

Various concepts go by the name *monad*.

Historically, going back to Gottfried Leibniz, “monad” is used to refer to a kind of “atom”, for him a mind-like simple substance. Derived from this is the idea of an “atom of space” (see also in Science of Logic the section *The Monad of Leibniz*). In roughly this sense the term is used in

In category theory and computer science a *monad* is a monoid acting on a category/type system, see at

To see this as an “atom” one observes that this is equivalently a lax 2-functor $\ast \longrightarrow Cat$ from the terminal category to the 2-category of categories and hence a "point" in some 2-categorical sense.

category: disambiguation

Revised on December 4, 2013 04:55:05
by Mike Shulman
(172.10.15.11)