Theorems · Definition · category theory

ModuleCat.homMk

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

Constructor for morphisms in ModuleCat R which takes as inputs a morphism between the underlying objects in AddCommGrpCat and the compatibility with the scalar multiplication.

Defined in

Mathlib.Algebra.Category.ModuleCat.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

Ring