I was unsure what notation to use, so I used english instead.
In Haskell a Functor f is characterized by a higher order function fmap :: (a -> b) -> (f a -> f b), which is required to satisfy the laws
fmap (g . f) = (fmap g) . (fmap f)
and
fmap id = id
where (.) :: (b -> c) -> (a -> b) -> (a -> c) is the function composition operator and id :: a -> a the identity function. Those are the laws the last two sentences try to phrase in english. In mathematics a functor F between categories C and D maps objects in C to objects in D and any morphism f: X -> Y in C to a morphism F f : F X -> F Y in D, in such a way that for morphisms f : X -> Y and g : Y -> Z in C one has F (g . f) = F g . F f and F id_X = id_{F X}. So you see Haskell and math notation are almost identical, although you can express the laws only as compiler rules in Haskell.
fmap (g . f) = (fmap g) . (fmap f)
and
fmap id = id
where (.) :: (b -> c) -> (a -> b) -> (a -> c) is the function composition operator and id :: a -> a the identity function. Those are the laws the last two sentences try to phrase in english. In mathematics a functor F between categories C and D maps objects in C to objects in D and any morphism f: X -> Y in C to a morphism F f : F X -> F Y in D, in such a way that for morphisms f : X -> Y and g : Y -> Z in C one has F (g . f) = F g . F f and F id_X = id_{F X}. So you see Haskell and math notation are almost identical, although you can express the laws only as compiler rules in Haskell.