DaoFP Chapter 13 Exercises

exercise

Exercises from DaoFP, Chapter 13. Solutions: DaoFP Chapter 13 Solutions. Index: Map of Content.

Exercise 13.2.1

Lambek’s lemma for coalgebras: show that the structure map $\tau :t\to Ft$ of the Terminal Coalgebra is an isomorphism.

Sources: DaoFP Exercise 13.2.1.

Solution: Solution 13.2.1

Exercise 13.2.2

For the identity functor on $\mathbf{Set}$, show every object is a fixed point, $\varnothing$ is the least and $1$ the greatest fixed point (Initial Algebra, Terminal Coalgebra).

Sources: DaoFP Exercise 13.2.2.

Solution: Solution 13.2.2

Exercise 13.2.3

Show that $\varnothing$ carries the Initial Algebra of the identity functor on $\mathbf{Set}$, and $1$ its Terminal Coalgebra.

Sources: DaoFP Exercise 13.2.3.

Solution: Solution 13.2.3