Theorems · Definition · linear algebra

LinearMap.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] →
                    {σ₁₂ : R →+* R₂} →
                      (p : Submodule R₂ M₂) → (f : M →ₛₗ[σ₁₂] M₂) → (∀ (c : M), f c ∈ p) → M →ₛₗ[σ₁₂] ↥p

A linear map f : M₂ → M whose values lie in a submodule p ⊆ M can be restricted to a linear map M₂ → p. See also LinearMap.codLift.

Defined in

Mathlib.Algebra.Module.Submodule.LinearMap

Cited by

61 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule