Thinking about the question of Lawver-Tierney's elementary topos, I thought it might be interesting to recount my one personal experience with Grothendieck. It was the summer of 1971. There was a logic conference in, IIRC, England, sponsored by NATO. Some people got together and decided to organize a logic counter-conference not sponsored by NATO. It took place at a residential school in a town called Uldum about 50 km or so south of Aarhus on the Jutland peninsula and they invited Grothendieck. Although he had at that time given up mathematics (he was present at the ICU Nice a year earlier, but when Bill Lawvere tried to talk to him—presumably about elementary toposes—G. said he wasn't interested), he accepted the invitation because of the circumstance. And gave a talk. Since I was spending that summer in Aarhus and had a car, I drove down to hear G. He first described the Verdier axioms in some detail. What logicians made of that I do not know. Then he turned to the audience and said, doesn't this remind you of set theory? Someone should study should study set theory from this point of view. I might add that for me, the Verdier axioms didn't look like set theory at all, but I am not a logician. At any rate, during the question period, I told him that there was a set of axioms for a topos that really did make it look like set theory. So G. Asked me to come to the blackboard and describe them. So I gave the L-T axioms except I added complete with generators to make them fully equivalent to Verdier's. He said that that was interesting and I sat down. That seems to have been the first time he had heard about the L-T axioms. Michael ​ 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