Dear category theorists, Sad news. My friend Eduardo Dubuc passed away Monday (July 27, 2026) after having a stroke. while teaching math at the University of Buenos-Aires. He was almost 84. He was visiting professor at UQAM until 1980, and professor at the UBA until his death. Eduardo received his Phd in 1969 from the University of Chicago under the supervision of Saunders MacLane with a thesis on Kan extension in enriched categories. His SLN monograph on the subject was the first systematic theory of enriched colimits and of enriched Kan extensions. Eduardo worked on a large variety of subjects throughout his life. https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en To illustrate the diversity of his work I will give a few examples. He introduced the Elevator Calculus for 2-categories around 1970, a precursor of Penrose diagrams and of string diagrams developed 15 years later by Ross Street and myself for applications to monoidal categories. He introduced and developed a theory of Tannaka duality for localic groups in a topos, with applications to the Grothendieck Galois theory developed by Myles Tierney and myself. He developed a theory of quasi-topoi with Jacques Penon, later included in the Sketches of an Elephant by P.T. Johnstone. He constructed the first full model of synthetic differential geometry in collaboration with Marta Bunge and Jacques Penon, it became the backbone of the book by Gonzalo Reyes and Ieke Moerdijk. He extended Stone duality to MV-algebras in collaboration with Roberto Cignoli et Daniele Mundici. He introduced a notion of Quillen model 2-category and a theory of 2-localizations with M.E. Descotte and Martin Szyld. He gave a construction of the 2-filtered bicolimits of bicategories in collaboration with Ross Street. His work has applications in every corner of category theory. Eduardo was a problem solver with the skills of a theory builder. He was a pleasant person to work with, eager to explore new territories. He was also a great math teacher. See you later Eduardo, André
Very sad news, Andre'! My sentiments to you and all of Eduardo's friends. --Valeria On Thu, Jul 30, 2026 at 4:29 AM Joyal, André via Categories < categories-list@categories.org.au> wrote:
Dear category theorists,
Sad news. My friend Eduardo Dubuc passed away Monday (July 27, 2026) after having a stroke. while teaching math at the University of Buenos-Aires. He was almost 84. He was visiting professor at UQAM until 1980, and professor at the UBA until his death.
Eduardo received his Phd in 1969 from the University of Chicago under the supervision of Saunders MacLane with a thesis on *Kan extension in enriched categories*. His SLN monograph on the subject was the first systematic theory of enriched colimits and of enriched Kan extensions. Eduardo worked on a large variety of subjects throughout his life.
https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en
To illustrate the diversity of his work I will give a few examples. He introduced the *Elevator Calculus* for 2-categories around 1970, a precursor of Penrose diagrams and of *string diagrams* developed 15 years later by Ross Street and myself for applications to monoidal categories. He introduced and developed a theory of *Tannaka duality for localic groups *in a topos, with applications to the Grothendieck Galois theory developed by Myles Tierney and myself. He developed a theory of *quasi-topoi* with Jacques Penon, later included in the *Sketches of an Elephant *by P.T. Johnstone. He constructed the first full model of *synthetic differential *geometry in collaboration with Marta Bunge and Jacques Penon, it became the backbone of the book by Gonzalo Reyes and Ieke Moerdijk. He extended *Stone duality to *MV-algebras in collaboration with Roberto Cignoli et Daniele Mundici. He introduced a notion of *Quillen model 2-category* and a theory of *2-localizations* with M.E. Descotte and Martin Szyld. He gave a construction of the 2-filtered bicolimits of bicategories in collaboration with Ross Street. His work has applications in every corner of category theory.
Eduardo was a problem solver with the skills of a theory builder. He was a pleasant person to work with, eager to explore new territories. He was also a great math teacher.
See you later Eduardo, André
_______________________________________________ Categories mailing list -- categories-list@categories.org.au To unsubscribe send an email to categories-list-leave@categories.org.au
Dear André and Everyone Thank you for conveying the sudden loss of our very dear friend. Excuse me for sharing a few of my vivid memories. Eduardo made talking mathematics exciting! We go back a long way. While I was a postdoc at the University of Illinois (Champaign - Urbana), Eduardo was with Saunders; I made the 120 mile train trip north to Chicago a few times. I think that is when we first met. Then came Bowdoin College, Maine, in the famous Summer of 1969. We shared the excitement of that meeting, especially Saunders' lectures each weekday morning. And there were the Day and Kelly papers in SLNM 106 to talk about! I was quite at home with the graduate student group attending the Bowdoin meeting. I had a big car so we would go touring and even swimming in the cold water. One time we decided to walk out on a sandy peninsula; I think one of us did some fishing. We were unaware of the high tides around there. When we decided to leave, we found we were on an island. One of us had a broken leg with a plaster cast that should not get wet. No worries! Eduardo put her up on his shoulders, I held up the leg, and we walked back with the water up to our waists. Eduardo was strong. Jack Duskin and I spent the academic year 1969-70 at Tulane University (New Orleans). They were having a year concentrating on category theory. Saunders was there with Eduardo for the first semester. Eduardo was finishing off his thesis. That is when we came up with "Dinatural Transformations" accompanied by examples. Saunders encouraged us to write it up. Some of my visits to Montréal overlapped with Eduardo's. We enjoyed talking mathematics, but also eating the great food followed by various kinds of farm fresh maple syrup and ice cream. Montréal weather is not like Buenos-Aires. One morning Eduardo awoke to his car windscreen covered in ice and snow. Strong-guy Eduardo cleared it with his bare hands. Not a good idea. It resulted in severe frost bite. Eduardo visited our rented house in Middletown Connecticut in the cold weather during my sabbatical at Wesleyan 1976-77. By that time we had found a good butcher in Middletown and even had non-homogenised non-pasteurised bottled milk delivered. Eduardo was determined to cook us a real Argentinian barbecue. This required visiting the butcher. But the meat was cut the wrong way! So Eduardo instructed the butcher on how to do it "properly". The barbecue proceeded in the snow, semi-dark, and minus 20 degree temperature on a little fire with two grills, and cooked very very slowly. It was delicious! We have lost a creative mathematician and captivating character. Ross On 30 Jul 2026, at 12:20 pm, Joyal, André via Categories <categories-list@categories.org.au> wrote: Dear category theorists, Sad news. My friend Eduardo Dubuc passed away Monday (July 27, 2026) after having a stroke. while teaching math at the University of Buenos-Aires. He was almost 84. He was visiting professor at UQAM until 1980, and professor at the UBA until his death. Eduardo received his Phd in 1969 from the University of Chicago under the supervision of Saunders MacLane with a thesis on Kan extension in enriched categories. His SLN monograph on the subject was the first systematic theory of enriched colimits and of enriched Kan extensions. Eduardo worked on a large variety of subjects throughout his life. https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en<https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en> To illustrate the diversity of his work I will give a few examples. He introduced the Elevator Calculus for 2-categories around 1970, a precursor of Penrose diagrams and of string diagrams developed 15 years later by Ross Street and myself for applications to monoidal categories. He introduced and developed a theory of Tannaka duality for localic groups in a topos, with applications to the Grothendieck Galois theory developed by Myles Tierney and myself. He developed a theory of quasi-topoi with Jacques Penon, later included in the Sketches of an Elephant by P.T. Johnstone. He constructed the first full model of synthetic differential geometry in collaboration with Marta Bunge and Jacques Penon, it became the backbone of the book by Gonzalo Reyes and Ieke Moerdijk. He extendedStone duality to MV-algebras in collaboration with Roberto Cignoli et Daniele Mundici. He introduced a notion of Quillen model 2-category and a theory of 2-localizations with M.E. Descotte and Martin Szyld. He gave a construction of the 2-filtered bicolimits of bicategories in collaboration with Ross Street. His work has applications in every corner of category theory. Eduardo was a problem solver with the skills of a theory builder. He was a pleasant person to work with, eager to explore new territories. He was also a great math teacher. See you later Eduardo, André _______________________________________________ Categories mailing list -- categories-list@categories.org.au<mailto:categories-list@categories.org.au> To unsubscribe send an email to categories-list-leave@categories.org.au<mailto:categories-list-leave@categories.org.au>
Thank you for letting us know this sad news, André. Just this year, my collaborators and I made use of Eduardo’s “adjoint triangle theorem” in the setting of exponentiability and the Beck-Chevalley condition: Eduardo Dubuc. Adjoint triangles. In Reports of the Midwest Category Seminar II, pages 69–91. Springer, 2006. I only met Eduardo a few times, but I always found him to be very friendly and congenial. Steve
On 29 Jul 2026, at 22:23, Joyal, André via Categories <categories-list@categories.org.au> wrote: Dear category theorists,
Sad news. My friend Eduardo Dubuc passed away Monday (July 27, 2026) after having a stroke. while teaching math at the University of Buenos-Aires. He was almost 84. He was visiting professor at UQAM until 1980, and professor at the UBA until his death.
Eduardo received his Phd in 1969 from the University of Chicago under the supervision of Saunders MacLane with a thesis on Kan extension in enriched categories. His SLN monograph on the subject was the first systematic theory of enriched colimits and of enriched Kan extensions. Eduardo worked on a large variety of subjects throughout his life.
https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en
To illustrate the diversity of his work I will give a few examples. He introduced the Elevator Calculus for 2-categories around 1970, a precursor of Penrose diagrams and of string diagrams developed 15 years later by Ross Street and myself for applications to monoidal categories. He introduced and developed a theory of Tannaka duality for localic groups in a topos, with applications to the Grothendieck Galois theory developed by Myles Tierney and myself. He developed a theory of quasi-topoi with Jacques Penon, later included in the Sketches of an Elephant by P.T. Johnstone. He constructed the first full model of synthetic differential geometry in collaboration with Marta Bunge and Jacques Penon, it became the backbone of the book by Gonzalo Reyes and Ieke Moerdijk. He extended Stone duality to MV-algebras in collaboration with Roberto Cignoli et Daniele Mundici. He introduced a notion of Quillen model 2-category and a theory of 2-localizations with M.E. Descotte and Martin Szyld. He gave a construction of the 2-filtered bicolimits of bicategories in collaboration with Ross Street. His work has applications in every corner of category theory.
Eduardo was a problem solver with the skills of a theory builder. He was a pleasant person to work with, eager to explore new territories. He was also a great math teacher.
See you later Eduardo, André
_______________________________________________ Categories mailing list -- categories-list@categories.org.au To unsubscribe send an email to categories-list-leave@categories.org.au
Dear André, I am extremely saddened by the news of Eduardo passing away. I happen to be one of the hundreds of very lucky students whom Eduardo, as the maestro that he was, taught how to think about and develop mathematics categorically. This no doubt shaped my subsequent research and teaching, and for it I will always be grateful and indebted. Eduardo's research was original and pioneering, deep and far reaching, and shall remain relevant and significant. I last interacted with him in person around a year ago, and he was still thinking about research. We had a nice mathematical discussion which we hoped to continue; sadly, this will now not happen. Marcelo On Thu, 30 Jul 2026 at 03:21, Joyal, André via Categories < categories-list@categories.org.au> wrote:
Dear category theorists,
Sad news. My friend Eduardo Dubuc passed away Monday (July 27, 2026) after having a stroke. while teaching math at the University of Buenos-Aires. He was almost 84. He was visiting professor at UQAM until 1980, and professor at the UBA until his death.
Eduardo received his Phd in 1969 from the University of Chicago under the supervision of Saunders MacLane with a thesis on *Kan extension in enriched categories*. His SLN monograph on the subject was the first systematic theory of enriched colimits and of enriched Kan extensions. Eduardo worked on a large variety of subjects throughout his life.
https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en
To illustrate the diversity of his work I will give a few examples. He introduced the *Elevator Calculus* for 2-categories around 1970, a precursor of Penrose diagrams and of *string diagrams* developed 15 years later by Ross Street and myself for applications to monoidal categories. He introduced and developed a theory of *Tannaka duality for localic groups *in a topos, with applications to the Grothendieck Galois theory developed by Myles Tierney and myself. He developed a theory of *quasi-topoi* with Jacques Penon, later included in the *Sketches of an Elephant *by P.T. Johnstone. He constructed the first full model of *synthetic differential *geometry in collaboration with Marta Bunge and Jacques Penon, it became the backbone of the book by Gonzalo Reyes and Ieke Moerdijk. He extended *Stone duality to *MV-algebras in collaboration with Roberto Cignoli et Daniele Mundici. He introduced a notion of *Quillen model 2-category* and a theory of *2-localizations* with M.E. Descotte and Martin Szyld. He gave a construction of the 2-filtered bicolimits of bicategories in collaboration with Ross Street. His work has applications in every corner of category theory.
Eduardo was a problem solver with the skills of a theory builder. He was a pleasant person to work with, eager to explore new territories. He was also a great math teacher.
See you later Eduardo, André
_______________________________________________ Categories mailing list -- categories-list@categories.org.au To unsubscribe send an email to categories-list-leave@categories.org.au
Dear André, Thank you for sharing the news. I only met Eduardo once, I believe at a CT. He was very kind and easy to talk with, and we had a nice math discussion. I'm sorry he's gone. David On Thu, Jul 30, 2026 at 7:57 AM Marcelo Fiore via Categories < categories-list@categories.org.au> wrote:
Dear André,
I am extremely saddened by the news of Eduardo passing away.
I happen to be one of the hundreds of very lucky students whom Eduardo, as the maestro that he was, taught how to think about and develop mathematics categorically. This no doubt shaped my subsequent research and teaching, and for it I will always be grateful and indebted.
Eduardo's research was original and pioneering, deep and far reaching, and shall remain relevant and significant. I last interacted with him in person around a year ago, and he was still thinking about research. We had a nice mathematical discussion which we hoped to continue; sadly, this will now not happen.
Marcelo
On Thu, 30 Jul 2026 at 03:21, Joyal, André via Categories < categories-list@categories.org.au> wrote:
Dear category theorists,
Sad news. My friend Eduardo Dubuc passed away Monday (July 27, 2026) after having a stroke. while teaching math at the University of Buenos-Aires. He was almost 84. He was visiting professor at UQAM until 1980, and professor at the UBA until his death.
Eduardo received his Phd in 1969 from the University of Chicago under the supervision of Saunders MacLane with a thesis on *Kan extension in enriched categories*. His SLN monograph on the subject was the first systematic theory of enriched colimits and of enriched Kan extensions. Eduardo worked on a large variety of subjects throughout his life.
https://scholar.google.com/citations?user=3fiEMcgAAAAJ&hl=en
To illustrate the diversity of his work I will give a few examples. He introduced the *Elevator Calculus* for 2-categories around 1970, a precursor of Penrose diagrams and of *string diagrams* developed 15 years later by Ross Street and myself for applications to monoidal categories. He introduced and developed a theory of *Tannaka duality for localic groups *in a topos, with applications to the Grothendieck Galois theory developed by Myles Tierney and myself. He developed a theory of *quasi-topoi* with Jacques Penon, later included in the *Sketches of an Elephant *by P.T. Johnstone. He constructed the first full model of *synthetic differential *geometry in collaboration with Marta Bunge and Jacques Penon, it became the backbone of the book by Gonzalo Reyes and Ieke Moerdijk. He extended *Stone duality to *MV-algebras in collaboration with Roberto Cignoli et Daniele Mundici. He introduced a notion of *Quillen model 2-category* and a theory of *2-localizations* with M.E. Descotte and Martin Szyld. He gave a construction of the 2-filtered bicolimits of bicategories in collaboration with Ross Street. His work has applications in every corner of category theory.
Eduardo was a problem solver with the skills of a theory builder. He was a pleasant person to work with, eager to explore new territories. He was also a great math teacher.
See you later Eduardo, André
_______________________________________________ Categories mailing list -- categories-list@categories.org.au To unsubscribe send an email to categories-list-leave@categories.org.au
_______________________________________________ Categories mailing list -- categories-list@categories.org.au To unsubscribe send an email to categories-list-leave@categories.org.au
participants (6)
-
David Spivak -
Joyal, André -
Marcelo Fiore -
Ross Street -
Steve Awodey -
Valeria de Paiva