Theorems · Theorem · category theory

AugmentedSimplexCategory.equivAugmentedCosimplicialObject_unitIso_inv_app_app

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C]
  (X : CategoryTheory.Functor (CategoryTheory.WithInitial SimplexCategory) C)
  (X_1 : CategoryTheory.WithInitial SimplexCategory),
  (AugmentedSimplexCategory.equivAugmentedCosimplicialObject.unitIso.inv.app X).app X_1 =
    (match X_1 with
      | CategoryTheory.WithInitial.of x => (CategoryTheory.Iso.refl (CategoryTheory.WithInitial.incl.comp X)).app x
      | CategoryTheory.WithInitial.star => CategoryTheory.Iso.refl (X.obj CategoryTheory.WithInitial.star)).inv

Defined in

Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic

Cited by

0 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category