Theorems · Theorem · linear algebra
Submodule.comap_strictMono_of_surjective
∀ {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}
[RingHomSurjective σ₁₂] {f : M →ₛₗ[σ₁₂] M₂}, Function.Surjective ⇑f → StrictMono (Submodule.comap f)- Defined in
- Mathlib.Algebra.Module.Submodule.Map
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- 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 · cited by 7,192
- StrictMonostatement · cited by 706
- Submodule.comapstatement · cited by 347
- RingHomSurjectivestatement and proof · cited by 220
- Submodule.giMapComapproof · cited by 11
- GaloisInsertion.strictMono_uproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.isCoatom_comap_iffproof · cited by 2
- isArtinian_of_surjectiveproof · cited by 2