Category Theory for Programmers Chapter 16: Yoneda Embedding

  1. Express the co-Yoneda embedding in Haskell, $ \mathscr{C}^{\mathrm{op}}, \mathbf{Set} \cong F(A) $.


  2. Show that the bijection we established between fromY and btoa is an isomorphism.

  3. Work out the Yoneda embedding for a Monoid. What functor corresponds to the single object? What natural transformations correspond to the morphism?

  4. What is the application of hte covariant Yoneda embedding to preorders?

  5. Yoneda embedding can be used to embed an artitrary functor category, $[\mathscr{C}, \mathscr{D}]$ in the functor category $[[\mathscr{C}, \mathscr{D}], \mathbf{Set}]$. Figure out how it works on morphisms.