Functor

[klequis]

Haskell's Functor class implements the functor laws.

fmap id      = id              -- identity
fmap (f . g) = fmap f . fmap g -- composition

These laws ensure that the containers shape is unchanged by fmap and that the container's contents are not re-arranged by the mapping operation.

source: https://www.haskell.org/tutorial/monads.html

[klequis]

In mathematics/category theory, a functor is a mapping between categories.

The set must have an identity and be composable.

for every object X in C (identity morphisms).

for all morphisms f:X -> Y and g:Y -> Z in C (composition)

source: wikipedia

[klequis]

unknown source

Rules of functor

1. Mapping the composition of two arrows is the same as composing the mapping of the fst arrow and the mapping of the 2nd arrow

2. The mapping of an objects identity is the same as the identity of the objects mapping.