Theorems · Theorem · category theory

CategoryTheory.Bicategory.whiskerLeft_hom_inv

∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {a b c : B} (f : a ⟶ b) {g h : b ⟶ c} (η : g ≅ h),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft f η.hom)
      (CategoryTheory.Bicategory.whiskerLeft f η.inv) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.CategoryStruct.comp f g)

Defined in: Mathlib.CategoryTheory.Bicategory.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.Bicategory

Mathlib docs Source Loogle LeanSearch

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.whiskerLeftstatement and proof · cited by 524
CategoryTheory.Iso.hom_inv_idproof · cited by 264
CategoryTheory.Bicategory.whiskerLeft_idproof · cited by 12
CategoryTheory.Bicategory.whiskerLeft_compproof · cited by 12

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Pseudofunctor.mapComp_id_right_homproof · cited by 4
CategoryTheory.Pseudofunctor.mapComp'₀₁₃_homproof · cited by 2
CategoryTheory.Bicategory.whiskerLeft_hom_inv_assocproof · cited by 2