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Theorems · Theorem · category theory

CategoryTheory.braiding_tensorUnit_left

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X : C),
  (β_ (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom
      (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).inv
Defined in
Mathlib.CategoryTheory.Monoidal.Braided.Basic
Cited by
7 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory
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Around this declaration

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CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst · cited by 7CartesianMonoidalCategory…CategoryTheory.braiding_inv_tensorUnit_left · cited by 2CategoryTheory.braiding_i…CategoryTheory.leftUnitor_inv_braiding · cited by 2CategoryTheory.leftUnitor…CategoryTheory.HopfObj.antipode_comul₂ · cited by 1HopfObj.antipode_comul₂CategoryTheory.braiding_tensorUnit_left_assoc · cited by 0CategoryTheory.braiding_t…CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.triangle · cited by 0PushoutProduct.triangleCategoryTheory.MonoidalCategory.Arrow.PushoutProduct.leftUnitor_naturality · cited by 0PushoutProduct.leftUnitor…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.MonoidalCategoryStruct.leftUnitor · cited by 437MonoidalCategoryStruct.le…CategoryTheory.MonoidalCategoryStruct.rightUnitor · cited by 397MonoidalCategoryStruct.ri…CategoryTheory.Iso.hom_inv_id · cited by 264Iso.hom_inv_idCategoryTheory.BraidedCategory.braiding · cited by 257BraidedCategory.braidingCategoryTheory.braiding_tenso…CITED BYCITES

Cites15

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Cited by7

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