Whereas my recollection (from those dear dim days beyond recall when I was present on a weekly basis for ND about that time) was that the terminology went from Mac Lane to May with operad to match monad as I recall, Mac Lane liked monad because of the philosophical connection Leibniz as philosopher not as mathematician? * Monad (Greek philosophy) a term used by ancient philosophers Pythagoras, Parmenides, Xenophanes, Plato, Aristotle, and Plotinus as a term for God or the first being, or the totality of all being. * Monism, the concept of "one essence" in the metaphysical and theological theory * Monad (Gnosticism), the most primal aspect of God in Gnosticism ****** Monadology, a book of philosophy by Gottfried Leibniz in which monads are a basic unit of perceptual reality * Monadologia Physica by Immanuel Kant * The Cup or Monad, a text in the Corpus Hermetica from the Wiki Johannes.Huebschmann@math.univ-lille1.fr wrote:
From my recollections, the terminology monad was suggested by P. May as a replacement for triple. The terminology was intended to match with "operad". At the time, S. Mac Lane has taken up that suggestion. In his book "Categories for the working mathematician" Mac Lane uses the terminology monad and comonad rather than triple and cotriple.
If Peter May participates in this board I am sure he will react.
Johannes
A question just came up at the Midland Graduate School (actually in the functional programming lecture): Where does the word monad come from?
I know that a monad is a monoid in the category of endofunctors, but what is the logic monoid => monad?
Btw, I frequently encounter monads in a categories of functors which are not endofunctors. An example are finite dimensional vectorspaces which can be constructed via a monoid in the category of functors FinSet -> Set, here I is the embedding and (x) can be constructed from the left kan extension and composition. The unit is given by the Kronecker delta and join can be constructed from Matrix multiplication. Should one call these beasts monads as well? Is there a good reference for this type of construction?
Cheers, Thorsten