Dear Uwe, I would suggest to decide how to talk about this after looking at: 1. Two places in the TAC reprint of Lawvere’s “FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES AND SOME ALGEBRAIC PROBLEMS IN THE CONTEXT OF FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES”, namely: (i) Item (2) (Page 8) of “1. Seven ideas introduced in the 1963 thesis”; (ii) A part of “2. Adjoint functors” on Pages 38-41. 2. Exercise 2 of Section 1 of “IV. Adjoints” from Mac Lane’s “CATEGORIES FOR THE WORKING MATHEMATICIAN” (It is on Page 84 in the 1st Edition, and on Page 86 in the 2nd Edition). Best regards, George From: Uwe Egbert Wolter <Uwe.Wolter@uib.no> Date: Monday, 23 June 2025 at 10:11 To: categories@mq.edu.au <categories@mq.edu.au> Subject: Lawvere's characterization of adjunctions CAUTION: This email originated outside the UCT network. Do not click any links or open attachments unless you know and trust the source. Dear all, What reference you would recommend for Lawvere's characterization of adjunctions by means comma categories? Best regards, Uwe 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>