Theorems · Theorem · category theory
CategoryTheory.Bicategory.triangle
∀ {B : Type u} [self : CategoryTheory.Bicategory B] {a b c : B} (f : a ⟶ b) (g : b ⟶ c),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator f (CategoryTheory.CategoryStruct.id b) g).hom
(CategoryTheory.Bicategory.whiskerLeft f (CategoryTheory.Bicategory.leftUnitor g).hom) =
CategoryTheory.Bicategory.whiskerRight (CategoryTheory.Bicategory.rightUnitor f).hom g- Defined in
- Mathlib.CategoryTheory.Bicategory.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Bicategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.Bicategory.whiskerRightstatement · cited by 531
- CategoryTheory.Bicategory.whiskerLeftstatement · cited by 524
- CategoryTheory.Bicategory.associatorstatement · cited by 405
- CategoryTheory.Bicategory.leftUnitorstatement · cited by 309
- CategoryTheory.Bicategory.rightUnitorstatement · cited by 308
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.leftUnitor_whiskerRightproof · cited by 7
- CategoryTheory.Bicategory.unitors_equalproof · cited by 5
- CategoryTheory.Bicategory.triangle_assoc_comp_rightproof · cited by 3
- CategoryTheory.Bicategory.triangle_assoc_comp_right_invproof · cited by 2
- CategoryTheory.Bicategory.triangle_assocproof · cited by 2
- CategoryTheory.FreeBicategory.liftHom₂_congrproof · cited by 1
- CategoryTheory.Bicategory.triangle_assoc_comp_leftproof · cited by 0