Theorems · Theorem · ring theory

Coalgebra.TensorProduct.assoc_tmul

∀ {R : Type u_5} {S : Type u_6} {M : Type u_7} {N : Type u_8} {P : Type u_9} [inst : CommSemiring R]
  [inst_1 : CommSemiring S] [inst_2 : Algebra R S] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid N]
  [inst_5 : AddCommMonoid P] [inst_6 : Module R M] [inst_7 : Module R N] [inst_8 : Module R P] [inst_9 : Module S M]
  [inst_10 : IsScalarTower R S M] [inst_11 : Coalgebra S M] [inst_12 : Module S N] [inst_13 : IsScalarTower R S N]
  [inst_14 : Coalgebra S N] [inst_15 : Coalgebra R P] (x : M) (y : N) (z : P),
  (Coalgebra.TensorProduct.assoc R S M N P) (x ⊗ₜ[S] y ⊗ₜ[R] z) = x ⊗ₜ[S] (y ⊗ₜ[R] z)

Defined in

Mathlib.RingTheory.Coalgebra.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModuleIsScalarTowerCoalgebraModuleIsScalarTowerCoalgebraCoalgebra