(1) should map \$$f \mapsto \langle f, id\rangle\$$

(2) should map \$$f \mapsto \lambda g. f \circ g\$$

If you don't mind some Haskell, Ralph Hinze and Daniel James have a nice paper [*Reason Isomorphically!* (2010)](http://www.cs.ox.ac.uk/ralf.hinze/publications/WGP10.pdf) that walks through all of these identities.