Theorems · Definition · category theory

CategoryTheory.CosimplicialObject.augment

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

Augment a cosimplicial object with an object.

Defined in

Mathlib.AlgebraicTopology.SimplicialObject.Basic

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category