Theorems · Definition · category theory

ModuleCat.isoMk

{R : Type u} →
  [inst : Ring R] →
    {M N : ModuleCat R} →
      (φ : (CategoryTheory.forget₂ (ModuleCat R) Ab).obj M ≅ (CategoryTheory.forget₂ (ModuleCat R) Ab).obj N) →
        (∀ (r : R),
            CategoryTheory.CategoryStruct.comp φ.hom (N.smul r) = CategoryTheory.CategoryStruct.comp (M.smul r) φ.hom) →
          (M ≅ N)

Constructor for isomorphisms in ModuleCat R taking an isomorphism in AddCommGrpCat and a compatibility condition.

Defined in

Mathlib.Algebra.Category.ModuleCat.Basic

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Ring