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fosco (Jan 25 2023 at 09:00):I am extremely inclined to believe that the Moore appearing "Eilenberg-Moore" is John Moore, algebraic topologist, but there's also Edward Moore, who worked in automata theory, and considering that Eilenberg was... well, he did both things with great profit, this seems a philological conundrum that can be solved only finding the original paper where Eilenberg and one of these Moore introduce the category of algebras for a monad. What is this paper called?
fosco (Jan 25 2023 at 09:05):(To make things worse, the two Moore were also almost exactly the same age with respect to Eilenberg, and born not so far from each other... I can't imagine how this problem is addressed for people who wrote with Erdős ;-) )
Bryce Clarke (Jan 25 2023 at 10:02):Adjoint functors and triples - Samuel Eilenberg, and John C. Moore
Bryce Clarke (Jan 25 2023 at 10:04):fosco said:
I am extremely inclined to believe that the Moore appearing "Eilenberg-Moore" is John Moore, algebraic topologist, but there's also Edward Moore, who worked in automata theory, and considering that Eilenberg was... well, he did both things with great profit, this seems a philological conundrum that can be solved only finding the original paper where Eilenberg and one of these Moore introduce the category of algebras for a monad. What is this paper called?
I'm very surprised that the original paper doesn't appear on the nLab. I'll add it there now.
fosco (Jan 25 2023 at 10:19):Very good, thanks.
Notification Bot (Jan 25 2023 at 10:30):Bryce Clarke has marked this topic as resolved.
Patrick Nicodemus (Jul 10 2023 at 08:11):Also recommend "Foundations of Relative Homological Algebra" which extends the ideas in this paper to develop the theory of homological algebra relatative to an adjunction, where objects in the image of the left adjoint are "free" and sequences that become split exact after applying the forgetful functor are "exact".
Patrick Nicodemus (Jul 10 2023 at 08:11):Also by Eilenberg and Moore and closely related to their work on monad algebras.
Patrick Nicodemus (Jul 10 2023 at 08:14):The paper "Adjoint functors and triples" might be the first mention of the 2-category of adjunctions as well