Theorems · Theorem · category theory
CategoryTheory.Bicategory.hom_inv_whiskerRight
∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {a b c : B} {f g : a ⟶ b} (η : f ≅ g) (h : b ⟶ c),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight η.hom h)
(CategoryTheory.Bicategory.whiskerRight η.inv h) =
CategoryTheory.CategoryStruct.id (CategoryTheory.CategoryStruct.comp f h)- Defined in
- Mathlib.CategoryTheory.Bicategory.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Bicategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.Bicategory.whiskerRightstatement and proof · cited by 531
- CategoryTheory.Iso.hom_inv_idproof · cited by 264
- CategoryTheory.Bicategory.comp_whiskerRightproof · cited by 14
- CategoryTheory.Bicategory.id_whiskerRightproof · cited by 13
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Pseudofunctor.mapComp_id_left_homproof · cited by 4
- CategoryTheory.Pseudofunctor.mapComp'₀₂₃_homproof · cited by 3
- CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_homproof · cited by 3
- CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_homproof · cited by 2
- CategoryTheory.Bicategory.hom_inv_whiskerRight_assocproof · cited by 1
- CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRightproof · cited by 1