DaoFP Chapter 10 Exercises

exercise

Exercises from DaoFP, Chapter 10. Solutions: DaoFP Chapter 10 Solutions. Index: Map of Content.

Exercise 10.3.1

Draw the naturality square of ${\varphi }_{xy}:\mathcal{D}(Lx,y)\to \mathcal{C}(x,Ry)$ in $x$.

Sources: DaoFP Exercise 10.3.1.

Solution: Solution 10.3.1

Exercise 10.3.2

$Lx$ is a representing object for which co-presheaf?

Sources: DaoFP Exercise 10.3.2.

Solution: Solution 10.3.2

Exercise 10.3.3

$Ry$ represents which presheaf?

Sources: DaoFP Exercise 10.3.3.

Solution: Solution 10.3.3

Exercise 10.5.1

Derive the counit of the coproduct adjunction $(+)⊣\Delta$ and the unit of the product adjunction $\Delta ⊣(\times )$.

Sources: DaoFP Exercise 10.5.1.

Solution: Solution 10.5.1

Exercise 10.5.2

Given $g:Lx\to y$, produce $x\to Ry$ using $\eta$ and functoriality of $R$.

Sources: DaoFP Exercise 10.5.2.

Solution: Solution 10.5.2

Exercise 10.5.3

Test the first triangle identity for currying: triangle (L (2, 'a')).

Sources: DaoFP Exercise 10.5.3.

Solution: Solution 10.5.3

Exercise 10.5.4

How to test the second triangle identity triangle' = fmap counit . unit :: R r x -> R r x?

Sources: DaoFP Exercise 10.5.4.

Solution: Solution 10.5.4

Exercise 10.9.1

What are the unit and counit of the free-monoid adjunction $F⊣U$?

Sources: DaoFP Exercise 10.9.1.

Solution: Solution 10.9.1

Exercise 10.9.2

Interpret a list of integers with the additive and with the multiplicative monoid.

Sources: DaoFP Exercise 10.9.2.

Solution: Solution 10.9.2