Theorems · Definition · category theory

CategoryTheory.SimplicialObject.augment

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

Augment a simplicial object with an object.

Defined in

Mathlib.AlgebraicTopology.SimplicialObject.Basic

Cited by

4 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category