Theorems · Definition · category theory

CategoryTheory.Functor.CoreMonoidal.ofLaxMonoidal

{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 D] →
            (F : CategoryTheory.Functor C D) →
              [inst_4 : F.LaxMonoidal] →
                [CategoryTheory.IsIso (CategoryTheory.Functor.LaxMonoidal.ε F)] →
                  [∀ (X Y : C), CategoryTheory.IsIso (CategoryTheory.Functor.LaxMonoidal.μ F X Y)] → F.CoreMonoidal

The Functor.CoreMonoidal structure given by a lax monoidal functor such that ε and μ are isomorphisms.

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

0 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.LaxMonoidalCategoryTheory.IsIsoCategoryTheory.IsIso