Theorems · Definition · commutative algebra

IsLocalizedModule.map

{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Submonoid R) →
      {M : Type u_2} →
        {M' : Type u_3} →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid M'] →
              [inst_3 : Module R M] →
                [inst_4 : Module R M'] →
                  (f : M →ₗ[R] M') →
                    [IsLocalizedModule S f] →
                      {N : Type u_6} →
                        {N' : Type u_7} →
                          [inst_6 : AddCommMonoid N] →
                            [inst_7 : AddCommMonoid N'] →
                              [inst_8 : Module R N] →
                                [inst_9 : Module R N'] →
                                  (g : N →ₗ[R] N') → [IsLocalizedModule S g] → (M →ₗ[R] N) →ₗ[R] M' →ₗ[R] N'

A linear map M →ₗ[R] N gives a map between localized modules Mₛ →ₗ[R] Nₛ.

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

60 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleIsLocalizedModuleAddCommMonoidAddCommMonoidModuleModuleIsLocalizedModule