Theorems · Theorem · linear algebra
Submodule.comap_map_mkQ
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p p' : Submodule R M),
Submodule.comap p.mkQ (Submodule.map p.mkQ p') = p ⊔ p'- Defined in
- Mathlib.LinearAlgebra.Quotient.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.mapstatement · cited by 614
- Submodule.comapstatement · cited by 347
- Submodule.mkQstatement and proof · cited by 232
- sup_commproof · cited by 165
- Submodule.ker_mkQproof · cited by 63
- Submodule.comap_map_eqproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- Submodule.le_of_map_mkQ_le_map_mkQ_of_le_jacobson_botproof · cited by 2
- Submodule.sup_eq_sup_smul_of_le_smul_of_le_jacobsonproof · cited by 2
- ContinuousLinearMap.isStrictMap_isClosed_range_iff_restrictproof · cited by 2
- Submodule.isClosed_mono_of_finiteDimensional_quotientproof · cited by 1
- Submodule.isClosed_sup_finiteDimensionalproof · cited by 1
- Submodule.eq_of_map_mkQ_eq_map_mkQ_of_le_jacobson_botproof · cited by 1
- IsLocalRing.map_mkQ_eqproof · cited by 1
- Module.finite_of_surjective_of_ker_le_nilradicalproof · cited by 0