Theorems · Theorem · category theory

CategoryTheory.FreeBicategory.normalize_naturality

∀ {B : Type u} [inst : Quiver B] {a b c : B} (p : Quiver.Path a b) {f g : CategoryTheory.FreeBicategory.Hom b c}
  (η : f ⟶ g),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.whiskerLeft ((CategoryTheory.FreeBicategory.preinclusion B).map { as := p }) η)
      (CategoryTheory.FreeBicategory.normalizeIso p g).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.FreeBicategory.normalizeIso p f).hom
      ((CategoryTheory.FreeBicategory.preinclusion B).map₂ (CategoryTheory.eqToHom ⋯))

The 2-isomorphism normalizeIso p f is natural in f.

Defined in

Mathlib.CategoryTheory.Bicategory.Coherence

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Quiver