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Theorems · Theorem · category theory

CategoryTheory.SymmetricCategory.symmetry_assoc

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.MonoidalCategory C}
  [self : CategoryTheory.SymmetricCategory C] (X Y : C) {Z : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (β_ X Y).hom (CategoryTheory.CategoryStruct.comp (β_ Y X).hom h) = h
Defined in
Mathlib.CategoryTheory.Monoidal.Braided.Basic
Cited by
11 results in Mathlib
Foundations
Depth 6 from the axioms · uses Quot.sound
Assumes
CategoryTheory.SymmetricCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Over.sectionsUncurry_sectionsCurry · cited by 2Over.sectionsUncurry_sect…CategoryTheory.AddGrpObj.tensorHom_neg_neg_add · cited by 2AddGrpObj.tensorHom_neg_n…CategoryTheory.GrpObj.tensorHom_inv_inv_mul · cited by 2GrpObj.tensorHom_inv_inv_…CategoryTheory.Over.sectionsCurry_sectionUncurry · cited by 2Over.sectionsCurry_sectio…CategoryTheory.AddGrpObj.add_neg_rev · cited by 1AddGrpObj.add_neg_revCategoryTheory.bijection_symm_apply_id · cited by 1CategoryTheory.bijection_…CategoryTheory.GradedObject.Monoidal.symmetry · cited by 1Monoidal.symmetryCategoryTheory.GrpObj.mul_inv_rev · cited by 1GrpObj.mul_inv_revCategoryTheory.MonoidalCategory.DayConvolution.symmetry · cited by 0DayConvolution.symmetryCategoryTheory.Monoidal.Reflective.isIso_tfae · cited by 0Reflective.isIso_tfaeCategoryTheory.SymmetricCategory.rightDistrib_of_leftDistrib · cited by 0SymmetricCategory.rightDi…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.BraidedCategory.braiding · cited by 257BraidedCategory.braidingCategoryTheory.SymmetricCategory · cited by 19CategoryTheory.SymmetricC…CategoryTheory.SymmetricCategory.symmetry · cited by 5SymmetricCategory.symmetrySymmetricCategory.symmetry_as…CITED BYCITES

Cites11

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Cited by11

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