Theorems · Inductive type · category theory

CategoryTheory.ModObj

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] → (M : C) → [CategoryTheory.MonObj M] → D → Type v₂

Given an action of a monoidal category C on a category D, an action of a monoid object M in C on an object X in D is the data of a map smul : M ⊙ₗ X ⟶ X that satisfies unitality and associativity with multiplication. See MulAction for the non-categorical version.

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

38 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory.MonoidalLeftActionCategoryTheory.MonObj