Theorems · Definition · category theory

CategoryTheory.Functor.Braided.ofChosenFiniteProducts

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_3 : CategoryTheory.CartesianMonoidalCategory D] →
            [inst_4 : CategoryTheory.BraidedCategory C] →
              [inst_5 : CategoryTheory.BraidedCategory D] →
                (F : CategoryTheory.Functor C D) → [CategoryTheory.Limits.PreservesFiniteProducts F] → F.Braided

A finite-product-preserving functor between Cartesian monoidal categories is braided. This is not made an instance because it would create a diamond for the monoidal structure on the identity and composition of functors.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.BraidedCategoryCategoryTheory.Limits.PreservesFiniteProducts