Theorems · Theorem · linear algebra

LinearMap.comap_codRestrict

∀ {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] {σ₂₁ : R₂ →+* R}
  (p : Submodule R M) (f : M₂ →ₛₗ[σ₂₁] M) (hf : ∀ (c : M₂), f c ∈ p) (p' : Submodule R ↥p),
  Submodule.comap (LinearMap.codRestrict p f hf) p' = Submodule.comap f (Submodule.map p.subtype p')

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

3 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule