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charset="utf-8" Content-Transfer-Encoding: quoted-printable It's curious to observe what all but appears as reluctance to acknowledge B= enabou's contribution. Even in adopting Benabou's terminology "monad", it seems to be generally ov= erlooked that he offered that term with a substantial mathematical motivati= on beyond the somewhat shallow alliteration on "monoid": Monads are the lax images of the unit 1. It seems hard to argue that this was already folklore when the term was pro= posed, given that even now it is hardly ever mentioned. It looks like Benabou was ahead of his time. On Fri, Nov 10, 2023 at 12:37=E2=80=AFAM JS Lemay > wrote: [[Sent on behalf of ross.street@mq.edu.au]] Dear Michael Thank you for filling in all that history. Heinrich Kleisli sent his paper to Saunders Mac Lane as editor. Saunders told us that he advised Heinrich Kleisli that Eilenberg-Moore had = solved the problem, as raised by Peter Hilton in his review of Huber's paper, on whether every = monad was generated by an adjunction. I presume Heinrich was unaware of E-M at the time, and vi= ve la difference! Another name that Saunders was testing, in his wonderful lectures at Bowdoi= n College (Maine) in the northern summer of 1969, was "triad". This was I think the second ru= n through on the subject of his Graduate Text in Math #5 (I believe the first was at the Australian Nat= ional University while I was in Illinois; and there was a third run at Tulane University where Eduardo Dubuc, Jack Du= skin and I were after Bowdoin). The triad name did not survive. Incidentally, Bob Walters used the term "de= vice" in his ANU thesis for the version that avoids the composite of the endofunctor with itself. When I mentioned that Jean B=C3=A9nabou was the first to use the name "mona= d" in a publication (SLNM 47), Bill Lawvere said Sammy Eilenberg had come up with that name first. As Bill= 's student, Anders Kock may know more about that. In my dealings with Sammy, he never mentioned such a claim, but I had not a= sked him either. Speaking of bicategories, I know Jean visited Chicago and did ask Saunders = permission to use "bicategory" since Saunders had used that term for a version of "factorizat= ion system". I do not know how much interaction Jean had with Sammy other than at catego= ry conferences. Ross ________________________________ From: Robert Pare Sent: Friday, November 10, 2023 7:03 AM To: Michael Barr, Prof. >; Categories mailing list > Subject: Re: The game of the name: Standard constructions, triples, monads,= fundamental constructions Mike, The usual caveat about memory applies. I came on the scene not long after this. My first big meeting was at the Battelle institute in Seattle in 1968. At that time Mac Lane was advocating forcefully for the name "triad" to replace "triple". Lambek was giving a series of talks on deductive systems and monads. His talk started "Let Trip be the category of standard constructions. A standard constructio= n is a quadruple (A, T, eta, mu)..." Bob ________________________________ From: Michael Barr, Prof. > Sent: November 8, 2023 5:19 PM To: categories@mq.edu.au > Subject: The game of the name: Standard constructions, triples, monads, fun= damental constructions CAUTION: The Sender of this email is not from within Dalhousie. People seemed to enjoy my history of the founding of TAC, so I thought you = might enjoy my sharing of other historical notes. This construction was introduced in Godement's book Th=C3=A9orie des faisce= aux in connection with his resolution of sheaves by "faisceaux mous" (soft = sheaves) which are an injective class. He called this "la construction sta= ndarde". It is not clear whether this was intended to name them or merely = describe them. At any rate, around 1960, Benno Eckmann and his students took as a name and called them standard con= structions. One of the students, Peter Huber, told me that they were havin= g trouble, in particular cases, verifying the associative law. And then he= noticed that in all the cases he knew, the functor T had the form UF, wher= e F --| U. He wondered if every adjoint pair gave rise to a standard const= ruction and proved that it did. Then another student, Heinrich Kleisli, sh= owed that the converse was also true. That gave us the well-known Kleisli = construction. In 1963 Samuel Eilenberg and John Moore published a monograph called Founda= tions of Relative Homological Algebra in which they used this construction = as basic. Only they didn't call them standard constructions; they called t= hem triples. I once asked Sammy why and he replied that it didn't seem lik= e an important concept and it didn't seem worth it to spend a lot of time w= orrying about the name. This is in stark contrast with the time he and Hen= ri Cartan spent thinking about the name for their basic sequences. There i= s a story, perhaps apocryphal, that their book was in proof stage before th= ey settled on the exact name. So triple was name Jon Beck and I were using in our joint work on homologic= al algebra. Then in 1966 there was a category meeting in Oberwohlfach and = there was a lot of discussion of a better name. The next bit of the story = comes out of my extremely fallible memory and could well be mistaken. One = day at lunch I was sitting next to Anders Koch and he asked what I thought = about the name monad. I thought (and still think!) it was a pretty good na= me and so he proposed it and the assembled crowd agreed and adopted it. I = would have too, but Jon rejected it. Why, I asked him. He did not think i= t a good name and refused to use it. He said there was no point in replaci= ng one bad name by another. Since we were collaborating and since he was e= ven more stubborn than me, that's they way it was. In our papers, Jon insi= sted on putting functions to the right of their arguments, just like revers= e Polish. Then we stopped collaborating and, by 1980, I think I was about ready to st= art using monad. But then TTT came along and the alliteration was just too= good to pass up. Charles Wells agreed on those grounds. And what about fundamental construction? I spent six and a half months at = the ETH in Zurich. A few days after I arrived, I got a phone call from Pet= er Huber, the aforementioned former student of Eckmann's. He had just rece= ived from Math Reviews a paper written by Jean-Marie Maranda that used that= term for the concept and Huber asked me if there was any way to stop that = proliferation of names. As far as I know, that was the only place that ter= m was ever used. Michael You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | Learn = more about Microsoft 365 Groups You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --000000000000368b7d0609f179fb Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
It's curious to observe what all but appears as reluctance to acknowle= dge Benabou's contribution.

Even in adopting Benabou's terminology "monad", it seems to = be generally overlooked that he offered that term with a substantial mathem= atical motivation beyond the somewhat shallow alliteration on "monoid&= quot;: 

Monads are the lax images of the unit 1. 

It seems hard to argue that this was already folklore when the term wa= s proposed, given that even now it is hardly ever mentioned.

It looks like Benabou was ahead of his time.


On Fri, Nov 10, 2023 at 12:37=E2=80= =AFAM JS Lemay <js.lemay@mq.edu.au= > wrote:
[[Sent on b= ehalf of  ross.street@mq.e= du.au]]

Dear Michae= l

Thank you f= or filling in all that history.

Heinrich Kl= eisli sent his paper to Saunders Mac Lane as editor.
Saunders to= ld us that he advised Heinrich Kleisli that Eilenberg-Moore had solved the = problem, 
as raised b= y Peter Hilton in his review of Huber's paper, on whether every monad was g= enerated
by an adjun= ction. I presume Heinrich was unaware of E-M at the time, and vive la difference! 

Another nam= e that Saunders was testing, in his wonderful lectures at Bowdoin College (= Maine)
in the nort= hern summer of 1969, was "triad". This was I think the second run= through on the subject of
his Graduat= e Text in Math #5 (I believe the first was at the Australian National Unive= rsity while I was in Illinois;
and there w= as a third run at Tulane University where Eduardo Dubuc, Jack Duskin and I = were after Bowdoin).
The triad n= ame did not survive. Incidentally, Bob Walters used the term "device&q= uot; in his ANU thesis for the
version tha= t avoids the composite of the endofunctor with itself.

When I ment= ioned that Jean B=C3=A9nabou was the first to use the name "monad"= ; in a publication (SLNM 47), 
Bill Lawver= e said Sammy Eilenberg had come up with that name first. As Bill's student,= Anders Kock may
know more a= bout that. 
In my deali= ngs with Sammy, he never mentioned such a claim, but I had not asked him ei= ther. 

Speaking of= bicategories, I know Jean visited Chicago and did ask Saunders permission = to use
"bicat= egory" since Saunders had used that term for a version of "factor= ization system". 
I do not kn= ow how much interaction Jean had with Sammy other than at category conferen= ces.

Ross=


From: = Robert Pare <R.Pare@Dal.Ca>
Sent: Friday, November 10, 2023 7:03 AM
To: Michael Barr, Prof. <barr.michael@mcgill.ca>; Categories mailing list= <categories@m= q.edu.au>
Subject: Re: The game of the name: Standard constructions, triples, = monads, fundamental constructions
 
Mike,

The usual c= aveat about memory applies.

I came on t= he scene not long after this. My first big meeting was at the <= /div>
Battelle in= stitute in Seattle in 1968. At that time Mac Lane was advocating
forcefully&= nbsp; for the name "triad" to replace "triple". Lambek = was giving a 
series of t= alks on deductive systems and monads. His talk started

"Let T= rip be the category of standard constructions. A standard construction = ;
is a quadru= ple (A, T, eta, mu)..."

Bob

From: Michael Barr, Prof. <barr.michael@mcgill.ca>
Sent: November 8, 2023 5:19 PM
To: catego= ries@mq.edu.au <categories@mq.edu.au>
Subject: The game of the name: Standard constructions, triples, mona= ds, fundamental constructions
 
CAUTION: The Sender = of this email is not from within Dalhousie.
People seemed to enjoy my history of the founding of TAC, so I thought you = might enjoy my sharing of other historical notes.

This construction was introduced in Godement's book Th=C3=A9orie des faisce= aux in connection with his resolution of sheaves by "faisceaux mous&qu= ot; (soft sheaves) which are an injective class.  He called this "= ;la construction standarde".  It is not clear whether this was intended to name them or merely describe them.  At any rate, arou= nd 1960,

 Benno Eckmann and his students took as a name and called them standar= d constructions.  One of the students, Peter Huber, told me that they = were having trouble, in particular cases, verifying the associative law.&nb= sp; And then he noticed that in all the cases he knew, the functor T had the form UF, where F --| U.  He wondered if e= very adjoint pair gave rise to a standard construction and proved that it d= id.  Then another student, Heinrich Kleisli, showed that the converse = was also true.  That gave us the well-known Kleisli construction. 

In 1963 Samuel Eilenberg and John Moore published a monograph called Founda= tions of Relative Homological Algebra in which they used this construction = as basic.  Only they didn't call them standard constructions; they cal= led them triples.  I once asked Sammy why and he replied that it didn't seem like an important concept and it di= dn't seem worth it to spend a lot of time worrying about the name.  Th= is is in stark contrast with the time he and Henri Cartan spent thinking ab= out the name for their basic sequences.  There is a story, perhaps apocryphal, that their book was in proof stage b= efore they settled on the exact name.

So triple was name Jon Beck and I were using in our joint work on homologic= al algebra.  Then in 1966 there was a category meeting in Oberwohlfach= and there was a lot of discussion of a better name.  The next bit of = the story comes out of my extremely fallible memory and could well be mistaken.  One day at lunch I was sitting ne= xt to Anders Koch and he asked what I thought about the name monad.  I= thought (and still think!) it was a pretty good name and so he proposed it= and the assembled crowd agreed and adopted it.  I would have too, but Jon rejected it.  Why, I asked him.&n= bsp; He did not think it a good name and refused to use it.  He said t= here was no point in replacing one bad name by another.  Since we were= collaborating and since he was even more stubborn than me, that's they way it was.  In our papers, Jon insisted on putting funct= ions to the right of their arguments, just like reverse Polish. 

Then we stopped collaborating and, by 1980, I think I was about ready to st= art using monad.  But then TTT came along and the alliteration was jus= t too good to pass up.  Charles Wells agreed on those grounds.

And what about fundamental construction?  I spent six and a half month= s at the ETH in Zurich.  A few days after I arrived, I got a phone cal= l from Peter Huber, the aforementioned former student of Eckmann's.  H= e had just received from Math Reviews a paper written by Jean-Marie Maranda that used that term for the concept and Huber asked = me if there was any way to stop that proliferation of names.  As far a= s I know, that was the only place that term was ever used.

Michael

 
 
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