Theorems · Theorem · linear algebra
Submodule.mkQ_surjective
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M),
Function.Surjective ⇑p.mkQ- Defined in
- Mathlib.LinearAlgebra.Quotient.Defs
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 85 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.
Cites9
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
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Submodule.mkQstatement · cited by 232
Cited by48
Results whose statement or proof uses this declaration.
- Ideal.toCotangent_surjectiveproof · cited by 15
- Module.FinitePresentation.fg_kerproof · cited by 6
- IsLocalRing.map_tensorProduct_mk_eq_topproof · cited by 4
- Module.isTorsionBySet_quotient_iffproof · cited by 4
- AddEquiv.isWeaklyRegular_congrproof · cited by 3
- Module.length_le_of_injectiveproof · cited by 3
- Module.equiv_free_prod_directSumproof · cited by 2
- Algebra.isEpi_iff_surjective_algebraMap_of_finiteproof · cited by 2
- Module.Relations.surjective_toQuotientproof · cited by 2
- Module.Basis.sumQuot_inrproof · cited by 2
- Module.isTorsionBy_quotient_iffproof · cited by 2