_Constant functors._

Let \\(C\\) and \\(D\\) be categories. Given any object \\(d\\) in \\(D\\), we can define the _constant functor_ \\(K_d: C \rightarrow D\\) on \\(d\\). This functor sends _every_ object \\(C\\) to \\(d \in Ob\ D\\), and _every_ morphism of \\(C\\) to the identity morphism on \\(d\\).

(a) Take the set \\(B\\) = {\\(T,F\\)}. Show that the constant functor \\(K_B: Set \rightarrow Set\\) obeys the two functor laws: preservation of composition and preservation of identities.

(b) Implement in Haskell the constant functor on the type Bool.

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Let \\(C\\) and \\(D\\) be categories. Given any object \\(d\\) in \\(D\\), we can define the _constant functor_ \\(K_d: C \rightarrow D\\) on \\(d\\). This functor sends _every_ object \\(C\\) to \\(d \in Ob\ D\\), and _every_ morphism of \\(C\\) to the identity morphism on \\(d\\).

(a) Take the set \\(B\\) = {\\(T,F\\)}. Show that the constant functor \\(K_B: Set \rightarrow Set\\) obeys the two functor laws: preservation of composition and preservation of identities.

(b) Implement in Haskell the constant functor on the type Bool.

***

[Next](https://forum.azimuthproject.org/discussion/2419/question-2-3-the-naturality-of-the-diagonal)

[Prev](https://forum.azimuthproject.org/discussion/2411/question-2-1-functors-out-of-set) [All](https://forum.azimuthproject.org/categories/exercises-applied-category-theory-course)