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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable 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_YQXPR01MB39277E9E194B79E108C881129CA8AYQXPR01MB3927CANP_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
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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