BM Category Theory 6: Functors & Examples


Discrete Category:  no other Morphism except the Identity Morphism. 

Functor between 2 categories : preserve structures.

6.2 Examples of functors

In-lining & Refactoring (in Pure Function)

1. In-lining: function f = function g
Replace everywhere in the program each f by g.

2. Re-factoring: In the program: {expressions}
We can define a function h = {expresions}, then use h throughout.

class Functor f where
\boxed {fmap : : (a \to b) \to (f a \to f b)}

Examples of Functors:

1. List

2. Reader

Functor (esp. Endo-functor) can be viewed as a Container where you can opetate on its content. Eg. Functor List [1 ..] = container of 1 2 3 … infinity, operared on it by generating (lazily) the next number.

Illustrations of Functors and Monad (Endo-functors): a “wrapped container”.,_applicatives,_and_monads_in_pictures.html#functors


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