Theorems · Theorem · linear algebra

ExteriorAlgebra.map_surjective_iff

∀ {R : Type u1} [inst : CommRing R] {M : Type u2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u4}
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] {f : M →ₗ[R] N},
  Function.Surjective ⇑(ExteriorAlgebra.map f) ↔ Function.Surjective ⇑f

A morphism of modules is surjective if and only the morphism of exterior algebras that it induces is surjective.

Defined in

Mathlib.LinearAlgebra.ExteriorAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule