Theorems · Theorem · category theory

CategoryTheory.LaxFunctor.mapComp_naturality_right

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  (self : CategoryTheory.LaxFunctor B C) {a b c : B} (f : a ⟶ b) {g g' : b ⟶ c} (η : g ⟶ g'),
  CategoryTheory.CategoryStruct.comp (self.mapComp f g) (self.map₂ (CategoryTheory.Bicategory.whiskerLeft f η)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (self.map f) (self.map₂ η))
      (self.mapComp f g')

Naturality of the lax functoriality constraint, on the right.

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.Lax

Cited by

2 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory