Universal Properties & Adjunctions
Posina Venkata Rayudu observed:
MacLane (1950) Duality for Groups ams.org/journals/bull/1950-56-06 ... doesn't cite Samuel (1948) Universal Mappings ... ams.org/journals/bull/1948-54-06 with its Universal Mapping Property...
Even more strange is that Mac Lane had REVIEWED Pierre Samuel's paper (needs an AMS login): mathscinet.ams.org/mathscinet-getitem?mr=0025152 Samuel probably also wrote the draft appendix to Bourbaki's "Algèbre" but it never appeared. This might be it: sites.mathdoc.fr/archives-bourbaki/PDF/041_iecnr_050.pdf Daniel Kan's 1958 paper "Adjoint Functors" was heavily citied withint a few years. Neither Kan nor Ehresmann cited Samuel. Google Scholar lists citations of Samuel in 1950+, 52, 57, 59+, 6-, 65+, 66, 70 (where + means twice) I haven't looked at all these but MacLane finally makes the connection with adjunctions in "Categorical algebra", Bull AMS 71 (1965) 40-106 pubs.ams.org/journals/bull/1965-71-01 These comments are based on fairly brief use of Google Scholar and other websites. It would be great if the few survivors from that time could correct me. Paul Taylor http://www.paultaylor.eu/delivery/261020-categories-history
Further to the thread, let me note that the importance of Samuel’s universal mapping property in his1948 paper as a true forerunner of Mac Lane’s “Duality of groups" was certainly known to many category theorists of the 1960s, and some of them may likely have been aware of the omission in the references of Mac Lane’s paper, without pointing to it explicitly — see, for example the opening sentences of Dieter Pumpluen’s article “Universelle und spezielle Probleme” in Mathematische Annalen 198:131–146, 1972, that is largely based on his (unpublished) 1967 lecture notes on category theory. As a student I learned from Pumpluen at the time that Samuel’s paper is also to be considered as a true forerunner of Freyd’s General Adjoint Functor Theorem—a fact that has been emphasized by Hans Porst, in his article “On free topological algebras", Cahiers 28(3):235–253, 1987, and more explicitly in more recent talks by him. Walter From: Paul Taylor via Categories <categories-list@categories.org.au> Date: Tuesday, October 20, 2026 at 4:12 AM To: categories-list@categories.org.au <categories-list@categories.org.au> Cc: Paul Taylor <categories@PaulTaylor.EU> Subject: [categories] Universal Properties & Adjunctions Posina Venkata Rayudu observed:
MacLane (1950) Duality for Groups ams.org/journals/bull/1950-56-06 ... doesn't cite Samuel (1948) Universal Mappings ... ams.org/journals/bull/1948-54-06 with its Universal Mapping Property...
Even more strange is that Mac Lane had REVIEWED Pierre Samuel's paper (needs an AMS login): mathscinet.ams.org/mathscinet-getitem?mr=0025152 Samuel probably also wrote the draft appendix to Bourbaki's "Algèbre" but it never appeared. This might be it: sites.mathdoc.fr/archives-bourbaki/PDF/041_iecnr_050.pdf Daniel Kan's 1958 paper "Adjoint Functors" was heavily citied withint a few years. Neither Kan nor Ehresmann cited Samuel. Google Scholar lists citations of Samuel in 1950+, 52, 57, 59+, 6-, 65+, 66, 70 (where + means twice) I haven't looked at all these but MacLane finally makes the connection with adjunctions in "Categorical algebra", Bull AMS 71 (1965) 40-106 pubs.ams.org/journals/bull/1965-71-01 These comments are based on fairly brief use of Google Scholar and other websites. It would be great if the few survivors from that time could correct me. Paul Taylor http://www.paultaylor.eu/delivery/261020-categories-history
participants (2)
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Paul Taylor -
Walter P Tholen