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Matteo Capucci (he/him) (Oct 19 2023 at 09:07):Is there a characterization of the morphisms inverted by a right adjoint?
I also know that units of this adjunction are invertible, i.e. that the left adjoint is ff.
Brendan Murphy (Oct 29 2023 at 17:41):If a map is inverted then it's "conjugate" to an isomorphism up to counts of the adjunction. Draw out the naturality square for the counit to see what I mean here. I'm not sure if there's anything better you can say, I think of it as basically meaning the counits generate the class of the inverted maps W (in that the localization at the class of counits will invert all of W)
Edit: this is for the case of a coreflective adjunction that you brought up, where the right adjoint in particular inverts the counits
Matteo Capucci (he/him) (Oct 30 2023 at 09:18):Cool, that's interesting to know