Re: Where does the term monad come from?

[Venanzio Capretta <vxc@Cs.Nott.AC.UK>]

The philosopher Gottfried Leibniz believed that every entity in the
Universe is a separate substance that doesn't interact with others. He
called these substances "monads". All properties and events that happen
to a monad are implicit in its nature from its creation. So if an apple
falls from a tree and bounces off my head, there is actually no contact:
the apple-monad bounces by itself without the help of my head and the
Venanzio-monad feels pain without the intervention of the apple. All
monads are synchronized from creation by the wisdom of God.
  This implies that every monad has an internal representation of every
entity in the universe and these representations can never influence
objects outside the monad.
  The analogy with our monads should be evident!



Thorsten Altenkirch wrote:
> 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
>
>