[stillkicking]

This explanation is useless imo because it expects the reader to already understand the weirdest part:

"If I have a function A -> B, how could I possibly get something that goes in the direction F B -> F A out of it?"

The answer to this is: given e.g. a function that accepts a B, i.e. `B -> ...` you can compose it with `A -> B` on the _input side_, to get a function that accepts an A, i.e. `A -> B` (+) `B -> ...` = `A -> ...`.

Once you've managed to get that across, you can start talking about contravariant functors. But expecting people to just intuit that from the condensed type signature is pedagogical nonsense.

[shikoba]

Saying without examples is a pedagogical nonsense, I can't argue, because I agree.

But if I provide the two typical examples Hom(A,) and Home(,A) and how they transport the arrows it starts to click.

There is also List which is a covariant functor. The stupid Home(unit,) which is the "identity" functor.

I could also add Hom(Bool,) which is the pair functor, ie Hom(Bool,A) is a tuple in AxA. A->AxA (or A->Him(Bool, A)) is a covariant functor.

Etc. Examples are the keys to understand the idea.