Theorems · Definition · commutative algebra

IsLocalizedModule.liftOfLE

{R : Type u_1} →
  [inst : CommSemiring R] →
    {M : Type u_2} →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {M₁ : Type u_6} →
            {M₂ : Type u_7} →
              [inst_3 : AddCommMonoid M₁] →
                [inst_4 : AddCommMonoid M₂] →
                  [inst_5 : Module R M₁] →
                    [inst_6 : Module R M₂] →
                      (S₁ S₂ : Submonoid R) →
                        S₁ ≤ S₂ →
                          (f₁ : M →ₗ[R] M₁) →
                            (f₂ : M →ₗ[R] M₂) → [IsLocalizedModule S₁ f₁] → [IsLocalizedModule S₂ f₂] → M₁ →ₗ[R] M₂

The natural map Mₛ →ₗ[R] Mₜ if s ≤ t (in Submonoid R).

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

6 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidAddCommMonoidModuleModuleIsLocalizedModuleIsLocalizedModule