Theorems · Theorem · category theory

CategoryTheory.LaxFunctor.mapComp_naturality_left_app

∀ {B : Type u_1} [inst : CategoryTheory.Bicategory B] (self : CategoryTheory.LaxFunctor B CategoryTheory.Cat)
  {a b c : B} {f f' : a ⟶ b} (η : f ⟶ f') (g : b ⟶ c) (X : ↑(self.obj a)),
  CategoryTheory.CategoryStruct.comp ((self.mapComp f g).toNatTrans.app X)
      ((self.map₂ (CategoryTheory.Bicategory.whiskerRight η g)).toNatTrans.app X) =
    CategoryTheory.CategoryStruct.comp ((self.map g).toFunctor.map ((self.map₂ η).toNatTrans.app X))
      ((self.mapComp f' g).toNatTrans.app X)

Naturality of the lax functoriality constraint, on the left.

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.Lax

Cited by

1 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory