On 4 Sep 2024, at 2:48 AM, P.T. Johnstone <ptj1000@cam.ac.uk> wrote: But I have heard from other sources that his main unhappiness about elementary toposes was annoyance that he had failed to spot the notion of subobject classifier (which he referred to as "the Lawvere element") that made the elementary development possible. If he had, SGA4 might have looked very different! Memory tells me that a subobject classifier does occur in SGA, perhaps in an example, with the \Omega notation which Lawvere and Tierney adopted. So Bill Lawvere was surprised when he heard Grothendieck's "Lawvere element" suggestion. Of course, the power that the cartesian closedness and the subobject classifier unleash was developed by Bill and Myles. Their's also was the ability to express a Grothendieck topology structure concisely as a monad on \Omega and to see it in Paul Cohen's forcing construction. Ross 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>