DaoFP Chapter 2 Exercises

exercise

Exercises from DaoFP, Chapter 2. Solutions: DaoFP Chapter 2 Solutions. Index: Map of Content.

Exercise 2.1.1

For $f:a\to b$, $g:b\to c$, show $((g\circ f)\circ -)=(g\circ -)\circ (f\circ -)$ as maps on arrows $h:x\to a$.

Sources: DaoFP Exercise 2.1.1.

Solution: Solution 2.1.1

Exercise 2.1.2

Convince yourself that the composition of post-compositions is associative.

Sources: DaoFP Exercise 2.1.2.

Solution: Solution 2.1.2

Exercise 2.1.3

Show pre-composition is composable with reversed order: $(-\circ (g\circ f))=(-\circ f)\circ (-\circ g)$.

Sources: DaoFP Exercise 2.1.3.

Solution: Solution 2.1.3

Exercise 2.3.1

What does $({\mathrm{id}}_a\circ -)$ do to arrows terminating in $a$? What does $(-\circ {\mathrm{id}}_a)$ do to arrows originating from $a$?

Sources: DaoFP Exercise 2.3.1.

Solution: Solution 2.3.1

Exercise 2.4.1

Show that any arrow from the Terminal Object is a Monomorphism.

Sources: DaoFP Exercise 2.4.1.

Solution: Solution 2.4.1

Exercise 2.5.1

Show that any arrow to the Terminal Object is an Epimorphism.

Sources: DaoFP Exercise 2.5.1.

Solution: Solution 2.5.1