Theorems · Theorem · category theory

CategoryTheory.CosimplicialObject.augment_hom_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (X : CategoryTheory.CosimplicialObject C) (X₀ : C)
  (f : X₀ ⟶ X.obj { len := 0 })
  (w :
    ∀ (i : SimplexCategory) (g₁ g₂ : { len := 0 } ⟶ i),
      CategoryTheory.CategoryStruct.comp f (X.map g₁) = CategoryTheory.CategoryStruct.comp f (X.map g₂)),
  (X.augment X₀ f w).hom.app { len := 0 } = f

Defined in

Mathlib.AlgebraicTopology.SimplicialObject.Basic

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category