Theorems · Theorem · linear algebra
exteriorPower.map_surjective
∀ {R : Type u} [inst : CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : AddCommGroup N] [inst_4 : Module R N] {f : M →ₗ[R] N},
Function.Surjective ⇑f → Function.Surjective ⇑(exteriorPower.map n f)If a linear map is surjective, then the map it induces on exterior powers is surjective.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidproof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Top.topproof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.