Theorems · Theorem · category theory
CategoryTheory.Bicategory.id_whiskerLeft
∀ {B : Type u} [self : CategoryTheory.Bicategory B] {a b : B} {f g : a ⟶ b} (η : f ⟶ g),
CategoryTheory.Bicategory.whiskerLeft (CategoryTheory.CategoryStruct.id a) η =
CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor f).hom
(CategoryTheory.CategoryStruct.comp η (CategoryTheory.Bicategory.leftUnitor g).inv)- Defined in
- Mathlib.CategoryTheory.Bicategory.Basic
- Cited by
- 9 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.
Cites8
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.Iso.invstatement · cited by 6,514
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.Bicategory.whiskerLeftstatement · cited by 524
- CategoryTheory.Bicategory.leftUnitorstatement · cited by 309
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.whiskerLeft_iffproof · cited by 2
- CategoryTheory.FreeBicategory.liftHom₂_congrproof · cited by 1
- CategoryTheory.Bicategory.leftUnitor_inv_naturalityproof · cited by 1
- CategoryTheory.Bicategory.leftUnitor_naturalityproof · cited by 1
- CategoryTheory.Bicategory.id_whiskerLeft_symmproof · cited by 0
- CategoryTheory.Bicategory.conjugateEquiv_associator_homproof · cited by 0
- CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_applyproof · cited by 0
- CategoryTheory.Bicategory.id_whiskerLeft_assocproof · cited by 0
- CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_applyproof · cited by 0