Because of the last messages that we interchanged, I was also expecting Thomas to recover. I think that I remember meeting him in Como 2000. He was sitting on a bench reading a draft of a paper that I had sent him. The paper was motivated by Thomas' work in collaboration with P. Lietz about the typed PCAs that induce realizability toposes. From the bench he invited me to talk about it. I don't remember the details of our chat, but I still feel grateful for his genuine interest. We did not meet often but each time we did, we disagreed on something about topos theory. As others have stressed, he was very kind, patient, and clever, so it was very informative and constructive to disagree with him. In 2015, the question of whether every pre-cohesive geometric morphism is molecular caught Thomas' attention, and we started to exchange emails more often. He had developed a sophisticated 'fibered view' of geometric morphisms (described “Fibered categories à la Jean Benabou”, Preprint; arxiv:1801.02927), and he attempted to apply it to the problem, but we could not answer the question. Again, we disagreed; he was convinced that there had to be non-molecular pre-cohesive topos and I am still hopeful that there is not. Anyway, since we could not answer the question, he proposed weaker forms of the problem and incited others (including myself) to look for counter-examples. See the 2021 papers by Hemelaer-Rogers, and by Garner-Streicher, and also Remark 3.8 in my 2022 paper edited by Thomas. All these examples show, as Thomas was suggesting, that as soon as you weaken the definition of pre-cohesive map a bit, there are non-molecular examples. Also around 2022 I showed that, over a Boolean base, pre-cohesive does imply molecular. Of course, this had a purely mathematical motivation, but I was very happy to use the result to continue arguing with Thomas about the original question. More recently, after the 2023 workshop on doctrines and fibrations that Thomas organized with Milly in Padova to celebrate Lawvere's life, we started discussing some of Bill's ideas about measurable cardinals. I was humbled to see how much Thomas knew about the classical literature on the subject. Of course, we disagreed on how much that literature should influence our work, and we had fun doing so until he fell ill. So we discussed other things, but he kept his good humour. M. El dom, 12 ene 2025 a las 19:30, Jens Hemelaer (<hemelaerjens@gmail.com<mailto:hemelaerjens@gmail.com>>) escribió: I am grateful for getting in touch with Thomas in 2020 through this mailing list. It was wonderful to care about the same problems and then approach them with different methods, and I will miss the joyfulness and passion that came through in his e-mails. My condolences to his family and friends, Jens On Tue, 7 Jan 2025 at 00:01, Peter LeFanu Lumsdaine <p.l.lumsdaine@gmail.com<mailto:p.l.lumsdaine@gmail.com>> wrote: Very sad news to start the New Year with. Like others, I was greatly influenced by Thomas’s work — I read his “Semantics” book cover to cover early in my PhD, and have had its meticulous proofs and terrible typography burned into my brain ever since. As others have noted, he and Martin Hofmann were the first to discover many of the ideas that later grew into homotopy type theory; I first met him (if I remember right) at the 2011 Oberwolfach meeting which brought Voevodsky’s work together with the established “old guard” of type theorists. Thomas was wonderful to talk maths with over a beer — gruff and opinionated, but always amiable and constructive in his disagreements. I didn’t see him much since Covid, and am sorry that I never got to discuss more recent developments with him, and now never will. With condolences to his family and friends, –Peter. You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, 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 mailing list group from Macquarie University. To take part in this conversation, 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 mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>