Documentation megathread

I'm trying to compile a thorough collection of everything currently documented and everything we still want to document. I'd also like to talk about a few other things other people brought up. This is sort of meant as a follow up to #1443. Another question that arrises, is if we really need documentation for every single one of these, or if some don't really make sense to have their own page. It might make sense to combine some of these as well (e.g. NonEmpty{List, Vector}).

Type classes:

• Kernel

  • Eq #1788
  • PartialOrder
  • Order
  • Semigroup
  • Monoid
  • Group
  • CommutativeSemigroup
  • Band
  • CommutativeMonoid
  • Semilattice
  • CommutativeGroup
  • BoundedSemilattice

• Functor

  • Invariant
  • Contravariant
  • BiFunctor
  • ProFunctor
  • Strong

• Core

  • Functor
  • Apply
  • Applicative
  • FlatMap
  • Monad
  • Foldable
  • Traverse
  • Reducible #1777
  • NonEmptyTraverse #1787
  • CoFlatMap
  • CoMonad
  • BiMonad
  • BiFoldable
  • BiTraverse
  • ApplicativeError
  • MonadError
  • CommutativeFlatMap
  • CommutativeMonad
  • InvariantMonoidal
  • SemigroupK
  • MonoidK
  • Alternative
  • Show #1789
  • Inject
  • InjectK
  • NotNull
  • Parallel

• Arrow

  • Arrow #1924
  • Category
  • Choice
  • CommutativeArrow
  • Compose

Data types

• Const
• Kleisli
• Cokleisli
• Id
• Eval #1816
• EitherK
• Tuple2K
• EitherT #1854
• OptionT
• State
• StateT
• OneAnd
• NonEmptyList #1971
• NonEmptyVector
• Validated
• FunctionK
• Either
• Ior #1822
• WriterT
• ReaderWriterStateT
• Nested

Other:

1. Laws. Briefly touched on in #510, currently there's no really good place to look for the laws of any given typeclass, I think we should definitely document and emphasize the laws on all the type classes.
2. Type class instances. Suggested in #1287, it would be really nice if we had some way to see all the defined instances for every type class we include in cats.

If I missed anything just tell me and I'll try to edit :)

Start by reviewing the checklist in this issue and the follow-up context from #1443, including the linked documentation issues and the sections on laws and type-class instances. Done would require agreeing on the documentation scope and organization, then covering the selected type classes and data types.