Theorems · Theorem · category theory
CategoryTheory.HopfObj.mul_antipode
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
[inst_2 : CategoryTheory.BraidedCategory C] (A : C) [inst_3 : CategoryTheory.HopfObj A],
CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul CategoryTheory.HopfObj.antipode =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.HopfObj.antipode CategoryTheory.HopfObj.antipode)
(CategoryTheory.CategoryStruct.comp (β_ A A).hom CategoryTheory.MonObj.mul)- Defined in
- Mathlib.CategoryTheory.Monoidal.Hopf_
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.tensorUnitproof · cited by 1,384
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftproof · cited by 915
- CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.HopfObj.antipode_antipodeproof · cited by 0