1

My question is the same as here, but I can't understand why the transformation from the identity functor to the composition of the adjoint functors is natural. I've tried proving explicitly that the diagram is commutative, but to no avail.

Snate
  • 202
  • Arnaud D., As seen in the comments of the answer, the asker understood himself why the diagram commutes. I get that by Yoneda lemma each transformation corresponds to a x-G(F(X)), but why is x-G(F(X)) natural? – Snate Oct 04 '19 at 10:40
  • 1
    For $u:X\to Y$, apply a naturality square for the bijection of appropriate hom-sets in the adjunction. – Berci Oct 04 '19 at 22:27

0 Answers0