Theorems · Theorem · ring theory
Submodule.IsCoideal.map_mkQ_comul_eq_zero
∀ {R : Type u_1} {C : Type u_2} {inst : CommRing R} {inst_1 : AddCommGroup C} {inst_2 : Module R C}
{inst_3 : CoalgebraStruct R C} {I : Submodule R C} [self : I.IsCoideal] ⦃x : C⦄,
x ∈ I → (TensorProduct.map I.mkQ I.mkQ) (CoalgebraStruct.comul x) = 0- Defined in
- Mathlib.RingTheory.Coalgebra.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Submodule.IsCoideal
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Cites14
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement · cited by 2,545
- HasQuotient.Quotientstatement · cited by 2,301
- TensorProduct.mapstatement · cited by 250
- Submodule.mkQstatement · cited by 232
- CoalgebraStructstatement and proof · cited by 230
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