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Cory Johnson (Sep 25 2022 at 15:49):is there a kind of generalized adjointness wherein only one of the categories remains the same throughout the string?
that is: if the left adjoint functor is F: C —> D, then the right adjoint might be G: E —> C, & right adjoint to that could be H: C —> F.
has this been defined before in the extant literature? looking for leads...
Dylan Braithwaite (Sep 25 2022 at 15:52):Is a [[relative adjoint functor]] what you're looking for?
Cory Johnson (Sep 25 2022 at 16:00):i suspect this is very close — thanks! i guess the one aspect it might miss (that i'm looking for) is the preservation of the notion of adjoint triple... to what extent is that still possible w/ relative adjoints?
Cory Johnson (Sep 25 2022 at 16:05):*especially if the auxiliary categories toggle (like in my example), therefore implying a J functor as well as a K functor... so perhaps there would be a tertiary relation (natural transformation?) b/t the J– & K– functors? i guess the triple would make sense if the J– & K–functors simply composed (since the domain of one does match the codomain of the other)?
Cory Johnson (Sep 25 2022 at 16:17):maybe this answers my question re: strings of relative adjoints — but it's too technical for me. https://mathoverflow.net/questions/281771/what-is-known-about-relative-adjunctions