Theorems · Theorem

CoassocSimps.assoc_comp_map_comm_comp_comul_comp_comul_assoc

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} {Q : Type u_9} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : AddCommMonoid Q]
  [inst_6 : Module R Q] [inst_7 : Coalgebra R M] (f : M →ₗ[R] N) (h : Q →ₗ[R] M),
  ↑(TensorProduct.assoc R M M N) ∘ₗ
      TensorProduct.map (↑(TensorProduct.comm R M M) ∘ₗ CoalgebraStruct.comul) f ∘ₗ CoalgebraStruct.comul ∘ₗ h =
    TensorProduct.map LinearMap.id (TensorProduct.map LinearMap.id f ∘ₗ ↑(TensorProduct.comm R M M)) ∘ₗ
      ↑(TensorProduct.assoc R M M M) ∘ₗ
        TensorProduct.map CoalgebraStruct.comul LinearMap.id ∘ₗ
          ↑(TensorProduct.comm R M M) ∘ₗ CoalgebraStruct.comul ∘ₗ h

Defined in

Mathlib.RingTheory.Coalgebra.CoassocSimps

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleCoalgebra