It depends on what you want to tell people. The idea per se is very simple. Once you have it, you see it is just exactly what every definition of adjoint functors says, put in arrow theoretic terms. . For references that typify Bill's thinking about it see his dissertation and his Category of Categories as Foundations. For a concise, authoritative treatment see Mac Lane's exercise 2 of Section IV.1 Adjoints, in Categories for the Working Mathematician 2nd ed. (It is also in the first ed but numbered differently and I do not have that on hand.) For a leisurely account using this idea from the ground up, see my book Elementary Categories, Elementary Toposes. Colin On Sat, Jun 21, 2025 at 7:25 AM Uwe Egbert Wolter <Uwe.Wolter@uib.no<mailto:Uwe.Wolter@uib.no>> wrote: 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 | 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>