Theorems · Theorem · category theory
CategoryTheory.Cat.associator_inv_app
∀ {B C D E : CategoryTheory.Cat} (F : B ⟶ C) (G : C ⟶ D) (H : D ⟶ E) (X : ↑B),
(CategoryTheory.Bicategory.associator F G H).inv.toNatTrans.app X = CategoryTheory.eqToHom ⋯- Defined in
- Mathlib.CategoryTheory.Category.Cat
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.NatTrans.appstatement · cited by 7,406
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Catstatement and proof · cited by 884
- CategoryTheory.eqToHomstatement · cited by 860
- CategoryTheory.Bundled.αstatement and proof · cited by 736
- CategoryTheory.Cat.Hom.toFunctorstatement and proof · cited by 531
- CategoryTheory.Bicategory.associatorstatement · cited by 405
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_appproof · cited by 1
- CategoryTheory.Pseudofunctor.mapComp'₀₁₃_inv_comp_mapComp'₀₂₃_hom_appproof · cited by 1
- CategoryTheory.OplaxFunctor.mapComp_assoc_left_appproof · cited by 1
- CategoryTheory.Pseudofunctor.mapComp'₀₂₃_hom_appproof · cited by 1
- CategoryTheory.Pseudofunctor.mapComp_assoc_left_hom_appproof · cited by 1
- CategoryTheory.LaxFunctor.mapComp_assoc_right_appproof · cited by 1
- CategoryTheory.Pseudofunctor.mapComp_assoc_right_inv_appproof · cited by 1
- CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom_appproof · cited by 1
- CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_inv_appproof · cited by 1
- CategoryTheory.Oplax.StrongTrans.whiskerLeft_naturality_comp_appproof · cited by 0