Triples vs Monads

[Peter May <may@math.uchicago.edu>]

Excerpt from my memorial address for Saunders MacLane, about events
around 1971 or 1972:

There is a terminological comment in Categories for the Working
Mathematician that I especially like and would like to share with you.
It concerns the substitution of monad for triple as the name of a
concept that all mathematicians here should know. He writes “The
frequent but unfortunate use of the word ‘triple’ in this sense has
achieved a maximum of needless confusion, what with the conflict with
ordered triple, plus the use of associated terms such as ‘triple derived
functors’ for functors which are not three times derived from anything
in the world. Hence the term ‘monad’.” One reason I like this passage is
that it is a beautiful illustration of the vividness of his writing, his
sheer verve. Another is that it is so characteristic of his manner of
arguing a point. But the third is personal. In the first draft he used
the word triple, and I won him over. I had just defined operads, and I
had coined that word to go well with monad.



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