DaoFP Chapter 19 Exercises

exercise

Exercises from DaoFP, Chapter 19. Solutions: DaoFP Chapter 19 Solutions. Index: Map of Content.

Exercise 19.1.1

Implement the internal hom for Day Convolution in Haskell (Monoidal Closed Category).

Sources: DaoFP Exercise 19.1.1.

Solution: Solution 19.1.1

Exercise 19.1.2

Implement the witnesses of the adjunction $[\mathcal{C},\mathbf{Set}](F\star G,H)\cong [\mathcal{C},\mathbf{Set}](F,[G,H{]}_{\mathrm{Day}})$ (Day Convolution).

Sources: DaoFP Exercise 19.1.2.

Solution: Solution 19.1.2

Exercise 19.3.1

Implement the Functor instance for Ran (Kan Extension).

Sources: DaoFP Exercise 19.3.1.

Solution: Solution 19.3.1

Exercise 19.3.2

Show the factorization $\alpha =\epsilon \cdot (\sigma \circ R)$ for $\sigma =(\alpha \circ L)\cdot (G\circ \eta )$ in the proof that $L\cong {\mathrm{Ran}}_R\mathrm{Id}$ (Kan Extension).

Sources: DaoFP Exercise 19.3.2.

Solution: Solution 19.3.2

Exercise 19.3.3

Implement the Functor instance for Codensity.

Sources: DaoFP Exercise 19.3.3.

Solution: Solution 19.3.3

Exercise 19.3.4

Implement the Applicative instance for Codensity.

Sources: DaoFP Exercise 19.3.4.

Solution: Solution 19.3.4

Exercise 19.4.1

Implement the Functor instance for Lan (Kan Extension).

Sources: DaoFP Exercise 19.4.1.

Solution: Solution 19.4.1

Exercise 19.4.2

Implement the Comonad instance for the density comonad data Density f c where D :: (f d -> c) -> f d -> Density f c (${\mathrm{Lan}}_{F}F$, Kan Extension).

Sources: DaoFP Exercise 19.4.2.

Solution: Solution 19.4.2