Theorems · Theorem · linear algebra
LinearMap.ker_pi
∀ {R : Type u} {M₂ : Type w} {ι : Type x} [inst : Semiring R] [inst_1 : AddCommMonoid M₂] [inst_2 : Module R M₂]
{φ : ι → Type i} [inst_3 : (i : ι) → AddCommMonoid (φ i)] [inst_4 : (i : ι) → Module R (φ i)]
(f : (i : ι) → M₂ →ₗ[R] φ i), (LinearMap.pi f).ker = ⨅ i, (f i).ker- Defined in
- Mathlib.LinearAlgebra.Pi
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement · cited by 7,192
- iInfstatement · cited by 1,690
- LinearMap.kerstatement and proof · cited by 848
- Submodule.extproof · cited by 204
- LinearMap.pistatement · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- mem_span_of_iInf_ker_le_kerproof · cited by 1
- Submodule.pi_liftQ_eq_liftQ_pistatement and proof · cited by 1
- Ideal.ker_tensorProductMk_quotientproof · cited by 0