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charset="utf-8" Content-Transfer-Encoding: quoted-printable Dear Francis, I greatly appreciate your input to the categories list regarding the contri= butions of Jean B=C3=A9nabou from half a century ago. I especially appreci= ated your "I downloaded a copy of these old texts via =E2=80=9CWeTransfer= =E2=80=9D and they will remain available during one week via the link https= ://we.tl/t-AwGwZkYcCq." I did so and now have them in four folders. However they are all in French= , whereas your three excellent volumes are in English. Is anyone volunteering to translate B=C3=A9nabou's texts into English? And on the matter of decidability, speaking as a complexiy theorist, is the= re a short summary of the essential points? Vaughan Pratt On Sun, Jan 21, 2024 at 1:34=E2=80=AFPM Francis Borceux > wrote: I had the privilege to have regular and often close contacts with Jean B=C3= =A9nabou during more than 50 years ; I learned much from him. It is a matter of fact that Jean did like very much lecturing, and he was d= oing that marvelously well =E2=80=A6 but he was quite reluctant to =C2=AB f= reeze =C2=BB a topic by writing it down. Early in the seventies, Jean gave several series of lectures at the Univers= ity of Louvain: on monads (called =E2=80=9Ctriples=E2=80=9D in those days),= multiplicative categories, distributors and toposes. Notes on these lectur= es were written down by some of the auditors and Jean accepted to have them= published in the preprints of the mathematics department. I downloaded a c= opy of these old texts via =E2=80=9CWeTransfer=E2=80=9D and they will remai= n available during one week via the link https://we.tl/t-AwGwZkYcCq. Some years later, Jean also gave a series of lectures on fibred categories = in Louvain-la-Neuve. As already mentioned by others, Jean-Roger Roisin wrot= e from these lectures a beautiful set of notes. These notes were never publ= ished because Jean, through the years, kept considering that he could still= improve and complete his results before their publication. When I wrote the three volumes of my =E2=80=9CHandbook of categorical algeb= ra=E2=80=9D, I wanted of course to include a chapter on fibred or indexed c= ategories: I chose fibred categories (Chapter 8 of Volume 2). Before sendin= g the chapter to the editor, I sent a copy of it to Jean, asking for his co= mments, but making clear that I was not at all asking permission to publish= this chapter, and that I would be the only one (with the referees) to deci= de of the final form of the text and take the responsibility of it. I defin= itely wanted to avoid a new endless story, in the vein of what was happenin= g to the Jean-Roger notes. I remember the upset answer that Jean gave me; he was focusing on three poi= nts. 1. I do not appreciate that you include a chapter containing many result= s of mine before I myself publish them. 2. At least, it is a relief to notice that your text reflects faithfully= my own views on this topic. 3. Thank you for putting emphasize on the notion of decidability, whose = importance does not seem to have been recognized by the categorical communi= ty. I am thus confident that this chapter reflects quite faithfully several ide= as of Jean, at the period where my book was written. Francis Francis Borceux 6 rue Fran=C3=A7ois 1490 Court-Saint-Etienne Belgique +32478390328 (portable) +3210614205 (fixe) francis.borceux@uclouvain.be 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 --00000000000093d15a060f83d2a7 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Dear Francis,

I greatly appreciate= your input to the categories list regarding the contributions of Jean B=C3= =A9nabou from half a century ago.  I especially appreciated your "= ;I downloaded a copy of these old texts via =E2=80=9CWeTransfer=E2=80=9D and they will remain a= vailable during one week via the link https://we.tl/t-AwGwZkYcCq."

I did so and now have them in four folders.  However= they are all in French, whereas your three excellent volumes are in Englis= h.

Is anyone volunteering to translate B=C3=A9= nabou's texts into English?

And on the matter of= decidability, speaking as a complexiy theorist, is there a short summary o= f the essential points?

Vaughan Pratt

On Sun, Jan 21, 2024 at 1:34=E2=80=AF= PM Francis Borceux <fran= cis.borceux@uclouvain.be> wrote:

 

I had the privilege to have regular and often close con= tacts with Jean B=C3=A9nabou during more than 50 years ; I learned muc= h from him.

 

It is a matter of fact that Jean did like very much lec= turing, and he was doing that marvelously well =E2=80=A6 but he was quite r= eluctant to =C2=AB freeze =C2=BB a topic by writing it down.

 

Early in the seventies, Jean gave several series of lec= tures at the University of Louvain: on monads (called =E2=80=9Ctriples=E2= =80=9D in those days), multiplicative categories, distributors and toposes. Notes on these lectures were written down by some of the audi= tors and Jean accepted to have them published in the preprints of the mathe= matics department. I downloaded a copy of these old texts via =E2=80=9CWeTr= ansfer=E2=80=9D and they will remain available during one week via the link https://we.tl/t-AwGwZkYcCq.

 

Some years later, Jean also gave a series of lectures o= n fibred categories in Louvain-la-Neuve. As already mentioned by others, Je= an-Roger Roisin wrote from these lectures a beautiful set of notes. These notes were never published because Jean, t= hrough the years, kept considering that he could still improve and complete= his results before their publication.

 

When I wrote the three volu= mes of my =E2=80=9CHandbook of categorical algebra=E2=80=9D, I wanted of co= urse to include a chapter on fibred or indexed categories: I chose fibred categories (Chapter 8 of Volume 2). Before sending the chap= ter to the editor, I sent a copy of it to Jean, asking for his comments, bu= t making clear that I was not at all asking permission to publish this chap= ter, and that I would be the only one (with the referees) to decide of the final form of the text and take t= he responsibility of it. I definitely wanted to avoid a new endless story, = in the vein of what was happening to the Jean-Roger notes.

 

I remember the upset answer that Jean gave me; he was f= ocusing on three points.

  1. I do not appreciate that you include a chapter containi= ng many results of mine before I myself publish them.<= /li>
  2. At least, it is a relief to notice that your text r= eflects faithfully my own views on this topic.
    3. Thank you for putting emphasize on the notion of decidabil= ity, whose importance does not seem to have been recognized by the categori= cal community.

I am t= hus confident that this chapter reflects quite faithfully several ideas of = Jean, at the period where my book was written.

 

Franci= s

 

Francis Borceux

6 rue Fran=C3=A7ois

1490 Court-Saint-Etie= nne

Belgique

+32478390328 (portabl= e)

+3210614205 (fixe)=

francis.borceux@uclouvain.be

 

 
 
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 g= roup files &nbs= p; |   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   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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