End ∫_c F(c,c) of a functor F: C^op × C → D is the universal dinatural wedge (equalizer of the two natural maps). Coend ∫^c is the dual coequalizer. For F = Hom, ∫_c Hom(c,c) = End(Id_C) = nat. endomorphisms of the identity functor.
End ∫_c F(c,c) of a functor F: C^op × C → D is the universal dinatural wedge (equalizer of the two natural maps). Coend ∫^c is the dual coequalizer. For F = Hom, ∫_c Hom(c,c) = End(Id_C) = nat. endomorphisms of the identity functor.