Theorems · Theorem · linear algebra

LinearMap.comap_restrict

∀ {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 R₂ M₂} {q : Submodule R M} {f : M₂ →ₛₗ[σ₂₁] M} (h : ∀ x ∈ p, f x ∈ q) (p' : Submodule R ↥q),
  Submodule.comap (f.restrict h) p' = Submodule.comap p.subtype (Submodule.comap f (Submodule.map q.subtype p'))

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule