Dear Paul, This is (a special case of) Lemma 2.1 in G.M. Kelly & Stephen Lack, Finite-product-preserving functors, Kan extensions, and strongly finitary 2-monads. Applied Categorical Structures 1:85-94, 1993. Steve. On 07/02/2011, at 11:25 AM, Paul Levy wrote:
Dear all,
Does the following result (which I learnt from Rasmus Mogelberg) appear in the literature somewhere?
Given categories C and D, a functor P : C^op x D --> Set and an adjunction F -| U : D --> C
the end over c in C of P(c,Fc) is (isomorphic to) the end over d in D of P(Ud,d).
Paul
-- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl
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