Timeline for Reference request: Who first proved that right adjoints preserve limits?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2021 at 6:44 | comment | added | user177829 | yeah apologies for incorrect answer, her is a quote from the appendix from Freyd's book. "Adjoint functors were defined by Kan [16], who borrowed their name from functional analysis and who exposed their properties as outlined in Exercises 3-G and 3-1. Except for Watts' theorem in 3-N [22], the adjoint functor theorems that are developed in the rest of the Chapter 3 exercises appeared in my dissertation [8]." | |
| Mar 29, 2021 at 17:43 | history | became hot network question | |||
| Mar 29, 2021 at 16:25 | comment | added | Dmitri Pavlov | @PaulTaylor: Additionally, Kan's 1956 paper also explicitly states that left/right adjoint functors preserve (co)limits as Theorems 13.8 and 13.8*. | |
| Mar 29, 2021 at 16:07 | comment | added | Dmitri Pavlov | @PaulTaylor: Daniel M. Kan defined limits and colimits in his 1956 paper “Adjoint functors” and proved that the (co)limit functor is left/right adjoint to the diagonal functor. Freyd's earliest paper (his Ph.D. thesis) is from 1960, there is no way he could be credited for (co)limits. | |
| Mar 29, 2021 at 15:41 | answer | added | Dmitri Pavlov | timeline score: 19 | |
| Mar 29, 2021 at 14:52 | comment | added | Paul Taylor | Whether the citation of Abelian Categories is correct, I don't know, but as I understand it, Peter Freyd is definitely the person who first recognised the unifying notion of "limit". After that, the fact that they are (preseved by) right adjoints is trivial. So @rft34, as a "new contributor", deserves the "correct answer" bonus. | |
| Mar 29, 2021 at 12:47 | comment | added | David White | Agreed. This does not answer the question. But, welcome to mathoverflow! | |
| Mar 29, 2021 at 11:59 | comment | added | user907616 | I think the adjoint functor theorems are rather a sort of converse to the statement I'm talking about. | |
| Mar 29, 2021 at 10:59 | comment | added | user177829 | Peter Freyd both for left and right adjoints in his book abelian Categories, an Introduction to the Theory of Functors its called Freyd's adjoint functor theorem | |
| Mar 29, 2021 at 9:47 | review | First posts | |||
| Mar 29, 2021 at 9:58 | |||||
| Mar 29, 2021 at 9:42 | history | asked | user907616 | CC BY-SA 4.0 |