Theorems · Theorem · category theory

CategoryTheory.SimplicialObject.augment_hom_zero

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

Defined in

Mathlib.AlgebraicTopology.SimplicialObject.Basic

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category