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feat: show that every polynomial functor is a (trivial) QPF (#10807)
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Every polynomial functor `P` is trivially also a quotient of a polynomial functor, namely, it's a quotient of itself through equality. That is, `abs` and `repr` are just the identity.
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alexkeizer committed Feb 21, 2024
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8 changes: 8 additions & 0 deletions Mathlib/Data/QPF/Multivariate/Basic.lean
Expand Up @@ -297,3 +297,11 @@ def ofEquiv {F F' : TypeVec.{u} n → Type*} [MvFunctor F'] [q : MvQPF F'] [MvFu
abs_map := by simp [q.abs_map, map_eq]

end MvQPF

/-- Every polynomial functor is a (trivial) QPF -/
instance MvPFunctor.instMvQPFObj {n} (P : MvPFunctor n) : MvQPF P where
P := P
abs := id
repr := id
abs_repr := by intros; rfl
abs_map := by intros; rfl

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