Theorems · Definition · category theory

CategoryTheory.IsMod_Hom

Deprecated since 2026-04-21Use CategoryTheory.IsModHom instead.

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] →
            (A : C) →
              [inst_4 : CategoryTheory.MonObj A] →
                {M N : D} → [CategoryTheory.ModObj A M] → [CategoryTheory.ModObj A N] → (M ⟶ N) → Prop

Alias of CategoryTheory.IsModHom. A morphism in D is a morphism of A-module objects if it commutes with the action maps

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

0 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory.MonoidalLeftActionCategoryTheory.MonObjCategoryTheory.ModObjCategoryTheory.ModObj