Theorems · Definition · category theory

linearEquivIsoModuleIso

{R : Type u} →
  [inst : Ring R] →
    {X Y : Type u} →
      [inst_1 : AddCommGroup X] →
        [inst_2 : AddCommGroup Y] →
          [inst_3 : Module R X] → [inst_4 : Module R Y] → (X ≃ₗ[R] Y) ≅ ModuleCat.of R X ≅ ModuleCat.of R Y

linear equivalences between Modules are the same as (isomorphic to) isomorphisms in ModuleCat

Defined in

Mathlib.Algebra.Category.ModuleCat.Basic

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModule