Theorems · Theorem

CoassocSimps.map_counit_comp_comul_right_assoc

∀ {R : Type u_1} {M : Type u_3} {P : Type u_5} {M' : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : AddCommMonoid P] [inst_4 : Module R P] [inst_5 : AddCommMonoid M']
  [inst_6 : Module R M'] [inst_7 : Coalgebra R M] (f : M →ₗ[R] M') (g : P →ₗ[R] M),
  TensorProduct.map f CoalgebraStruct.counit ∘ₗ CoalgebraStruct.comul ∘ₗ g =
    TensorProduct.map f LinearMap.id ∘ₗ ↑(TensorProduct.rid R M).symm ∘ₗ g

Defined in

Mathlib.RingTheory.Coalgebra.CoassocSimps

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleCoalgebra