Theorems · Theorem · category theory

CategoryTheory.Lax.LaxTrans.naturality_id

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G : CategoryTheory.LaxFunctor B C} (self : CategoryTheory.Lax.LaxTrans F G) (a : B),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (self.app a) (G.mapId a))
      (self.naturality (CategoryTheory.CategoryStruct.id a)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor (self.app a)).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor (self.app a)).inv
        (CategoryTheory.Bicategory.whiskerRight (F.mapId a) (self.app a)))

Lax unity.

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax

Cited by

2 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory