Theorems · Theorem · linear algebra
Submodule.map_comap_le
∀ {R : Type u_1} {R₂ : Type u_3} {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] {σ₁₂ : R →+* R₂}
[inst_6 : RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (q : Submodule R₂ M₂), Submodule.map f (Submodule.comap f q) ≤ q- Defined in
- Mathlib.Algebra.Module.Submodule.Map
- Cited by
- 6 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.
Cites11
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
- Submodule.mapstatement · cited by 614
- Submodule.comapstatement · cited by 347
- RingHomSurjectivestatement and proof · cited by 220
- GaloisConnection.l_u_leproof · cited by 36
- Submodule.gc_map_comapproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.map_comap_eqproof · cited by 18
- Module.End.generalized_eigenvec_disjoint_range_kerproof · cited by 1
- Submodule.comap_lt_of_lt_map_of_injectiveproof · cited by 1
- LinearMap.iterateMapComap_le_succproof · cited by 1
- Module.End.iSup_maxGenEigenspace_eq_topproof · cited by 1