Theorems · Inductive type · category theory

CategoryTheory.Functor.LaxMonoidal

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [CategoryTheory.MonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [CategoryTheory.MonoidalCategory D] → CategoryTheory.Functor C D → Type (max u₁ v₂)

A functor F : C ⥤ D between monoidal categories is lax monoidal if it is equipped with morphisms ε : 𝟙_ D ⟶ F.obj (𝟙_ C) and μ X Y : F.obj X ⊗ F.obj Y ⟶ F.obj (X ⊗ Y), satisfying the appropriate coherences.

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

133 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 4 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory