Theorems · Definition · category theory
CategoryTheory.Bicategory.associator
{B : Type u} →
[self : CategoryTheory.Bicategory B] →
{a b c d : B} →
(f : a ⟶ b) →
(g : b ⟶ c) →
(h : c ⟶ d) →
CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f g) h ≅
CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp g h)The associator isomorphism: (f ≫ g) ≫ h ≅ f ≫ g ≫ h
- Defined in
- Mathlib.CategoryTheory.Bicategory.Basic
- Cited by
- 405 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- CategoryTheory.Bicategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Isostatement · cited by 3,963
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
Cited by503
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.mateEquivproof · cited by 24
- CategoryTheory.Cat.associator_hom_appstatement · cited by 22
- CategoryTheory.Cat.associator_inv_appstatement · cited by 17
- CategoryTheory.Bicategory.LeftExtension.whiskerproof · cited by 15
- CategoryTheory.Bicategory.LeftLift.whiskerproof · cited by 15
- CategoryTheory.Bicategory.whiskerRight_compstatement · cited by 14
- CategoryTheory.Bicategory.mateEquiv_apply'proof · cited by 9
- CategoryTheory.Bicategory.RightLift.whiskerproof · cited by 8
- CategoryTheory.Bicategory.comp_whiskerLeftstatement · cited by 7
- CategoryTheory.Bicategory.leftUnitor_whiskerRightstatement and proof · cited by 7
- CategoryTheory.Bicategory.Adjunction.homEquiv₁proof · cited by 7
- CategoryTheory.Bicategory.trianglestatement · cited by 7
Showing the 200 most cited of 503.