Peter May wrote:

I never claimed to invent the term monad. I did invent the term operad, as a portmanteau of operation and monad. Peter May

which I am happy to confirm I think I was there at the time or at least nearby jim Rainer, Is this covered in your memoir of those miravulaous years? jim

I hope I can add some jigsaw pieces towards the history of the term "monad" in category theory without offending anyone. 1) It is clearly a fact that the term "monad" is used in Benabou's paper SLNM 47 (1967). He recognized that it is a morphism of bicategories from the terminal category 1. 2) I have a clear memory that Mac Lane told me (perhaps at Chicago while I was a postdoc at Champaign-Urbana 1968-69) that Benabou courteously asked him (possibly by airmail, maybe by phone call, maybe at a conference) whether Mac Lane would mind whether he used the term "bicategory" in the sense we now use it. Mac Lane had used "bicategory" to mean a category with two distinguished classes of morphisms: roughly speaking, what we now call a category with a factorization system. Mac Lane told Benabou he did not mind. So Benabou used it in SLNM 47. 3) Less clearly I remember Mac Lane said Benabou also suggested the term "monad" for use in SLNM 47. 4) It is again my clear memory that, in his lecture marathon at the Summer School on Category Theory at Bowdoin College (Maine, mid-1969), Mac Lane expressed strong dislike for the term "triple" but had not really settled on a term. Mac Lane actually used the term "triad" in his lectures at Bowdoin. 5) At CT08, Lawvere told me Eilenberg suggested the term "monad". Best wishes, Ross

[Note from moderator: this thread has strayed; although this post is allowed, comments closer to categories (not Kant's) are preferred.] Reference to Leibniz is nice, and so is going back even more in history. Going forward into modern history leads to problems of who actually caused what. Probably because we then tend to mix history and politics. Anyway, also having googled, I found this about Leibniz: §. 1. Die Monaden (Das Worte Monade oder Monas) wovon wir allhier reden werden / sind nichts anders als einfache Substanzen / woraus die zusammen gesetzten Dinge oder composita bestehen. Unter dem Wort / einfach / verstehet man dasjenige / welches keine Teile hat. "sind nichts anders als einfache Substanzen" "is nothing but simple substances" They are, but it is not a mathematical statement. "woraus die zusammen gesetzten Dinge oder composita bestehen" "using which you put them together or compose(!) them together" Now he is cooking. Monad compositions are important. Leibniz and Beck working together, I like it. This is closer to mathematics. "verstehet man dasjenige / welches keine Teile hat" "is to be understood as something which doesn't have subparts" I am sure there are non-trivial monads which are not composed (in Beck's sense) by other non-trivial monads. But more interestingely, composed monads are indeed monads, and even worse (from leibniz point of view) submonads do exist, like the filter monad being submonad to the ultrafilter monad (with the astonishing fact, yes, I know, I am repreating myself, that their respective algebras are Scott lattices and compact Hausdorff spaces). So, basically I like Leibniz, even if he was wrong at this point. History is not easy. We say "Rome was destroyed" and we frequently say by the goths. Saying that leads us to ask "how could it be destroyed". Seldom do we hear "how could it stay alive so long". Best, Patrik PS "Monas" seems mostly to be used for a sailing boat, the "Kiel", and "the Mona" is Louvre in Paris.