Theorems · Theorem · linear algebra

ExteriorAlgebra.leftInverse_map_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} {g : N →ₗ[R] M},
  Function.LeftInverse ⇑(ExteriorAlgebra.map g) ⇑(ExteriorAlgebra.map f) ↔ Function.LeftInverse ⇑g ⇑f

For a linear map f from M to N, ExteriorAlgebra.map g is a retraction of ExteriorAlgebra.map f iff g is a retraction of f.

Defined in

Mathlib.LinearAlgebra.ExteriorAlgebra.Basic

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule