Re: Where does the term monad come from?

[Johannes.Huebschmann@math.univ-lille1.fr]

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
>
>
>