Theorems · Theorem · linear algebra
LinearMap.ker_le_comap
∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
{p : Submodule R₂ M₂} (f : M →ₛₗ[τ₁₂] M₂), f.ker ≤ Submodule.comap f p- Defined in
- Mathlib.Algebra.Module.Submodule.Ker
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- LinearMap.kerstatement and proof · cited by 848
- Submodule.comapstatement · cited by 347
- LinearMap.mem_kerproof · cited by 66
Cited by5
Results whose statement or proof uses this declaration.
- LinearMap.comap_eq_sup_ker_of_disjointproof · cited by 1
- LinearMap.ker_le_of_iterateMapComap_eq_succproof · cited by 1
- Function.Exact.exact_mapQ_iffproof · cited by 1
- Submodule.comap_covBy_of_surjectiveproof · cited by 1
- Submodule.biSup_comap_eq_top_of_surjectiveproof · cited by 1