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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable 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=E9orie des faisceaux= in connection with his resolution of sheaves by "faisceaux mous" (soft she= aves) which are an injective class. He called this "la construction standa= rde". It is not clear whether this was intended to name them or merely des= cribe 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 --_000_YQXPR01MB26462A53AF168582C845A0F2E5AFAYQXPR01MB2646CANP_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
Mike,

The usual caveat about = memory applies.

I came on the scene not long after this. My firs= t big meeting was at the 
Battelle institute in Seattle in 1968. At that t= ime 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 const= ructions. A standard construction 
is a quadruple (A, T, eta, mu)..."

Bob

From: Michael Barr, Prof. &= lt;barr.michael@mcgill.ca>
Sent: November 8, 2023 5:19 PM
To: categories@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=E9orie des faisceaux= in connection with his resolution of sheaves by "faisceaux mous"= (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

 
 
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   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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