Theorems · Theorem · category theory

CategoryTheory.OplaxFunctor.mapComp_id_left_assoc

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  (F : CategoryTheory.OplaxFunctor B C) {a b : B} (f : a ⟶ b) {Z : F.obj a ⟶ F.obj b}
  (h : CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.id (F.obj a)) (F.map f) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.mapComp (CategoryTheory.CategoryStruct.id a) f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapId a) (F.map f)) h) =
    CategoryTheory.CategoryStruct.comp (F.map₂ (CategoryTheory.Bicategory.leftUnitor f).hom)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor (F.map f)).inv h)

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.Oplax

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory