Theorems · Definition · category theory

CategoryTheory.SymmetricCategory.ofFaithful

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          [inst_3 : CategoryTheory.MonoidalCategory D] →
            [inst_4 : CategoryTheory.BraidedCategory C] →
              [inst_5 : CategoryTheory.SymmetricCategory D] →
                (F : CategoryTheory.Functor C D) → [F.Braided] → [F.Faithful] → CategoryTheory.SymmetricCategory C

A braided category with a faithful braided functor to a symmetric category is itself symmetric.

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.SymmetricCategoryCategoryTheory.Functor.BraidedCategoryTheory.Functor.Faithful