6 Nov
2000
6 Nov
'00
2:58 a.m.
Mike Barr wrote:
In this discussion of adjoint cylinders, I haven't noticed anyone pointing out that when L --| F --| R, then FL = Id (I use = for natural equivalence here) iff FR = Id. Dusko told me earlier this year that it was in his thesis, but I would not be surprised if it were older than that. Here is a simple proof....
Here is an even simpler one: FL is left adjoint to FR, by composability of adjoints; the identity functor is left adjoint to itself. Peter Johnstone