From Tealeaves Require Export
  Classes.Functor
  Functors.Early.Batch.

Class ToBatch (T: Type → Type) :=
  toBatch: ∀ A A', T A → Batch A A' (T A').

#[global] Arguments toBatch {T}%function_scope {ToBatch}
  {A A'}%type_scope _.

Class TraversableFunctor
  (T: Type → Type)
  `{ToBatch_T: ToBatch T} :=
  { trf_extract: ∀ (A: Type),
      extract_Batch ∘ toBatch = @id (T A);
    trf_duplicate: ∀ (A B C: Type),
      cojoin_Batch ∘ toBatch =
        map (toBatch (A' := C)) ∘ toBatch (A := A) (A' := B)
  }.