Theorems · Theorem · ring theory
Coalgebra.coassoc_apply
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
[inst_3 : Coalgebra R A] (a : A),
(TensorProduct.assoc R A A A) ((LinearMap.rTensor A CoalgebraStruct.comul) (CoalgebraStruct.comul a)) =
(LinearMap.lTensor A CoalgebraStruct.comul) (CoalgebraStruct.comul a)- Defined in
- Mathlib.RingTheory.Coalgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
- LinearMap.rTensorstatement · cited by 266
- LinearMap.lTensorstatement · cited by 203
- CoalgebraStruct.comulstatement · cited by 118
- Coalgebrastatement and proof · cited by 112
Cited by1
Results whose statement or proof uses this declaration.
- Coalgebra.coassoc_symm_applyproof · cited by 1