Theorems · Theorem · algebraic topology

CategoryTheory.SimplicialObject.Splitting.IndexSet.fac_pull

∀ {Δ : SimplexCategoryᵒᵖ} (A : CategoryTheory.SimplicialObject.Splitting.IndexSet Δ) {Δ' : SimplexCategoryᵒᵖ}
  (θ : Δ ⟶ Δ'),
  CategoryTheory.CategoryStruct.comp (A.pull θ).e
      (CategoryTheory.Limits.image.ι (CategoryTheory.CategoryStruct.comp θ.unop A.e)) =
    CategoryTheory.CategoryStruct.comp θ.unop A.e

Defined in: Mathlib.AlgebraicTopology.SimplicialObject.Split
Cited by: 2 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Oppositestatement and proof · cited by 8,081
Opposite.unopstatement · cited by 2,231
SimplexCategorystatement and proof · cited by 2,204
Quiver.Hom.unopstatement and proof · cited by 903
CategoryTheory.Epistatement · cited by 688
CategoryTheory.Limits.image.ιstatement · cited by 104
CategoryTheory.SimplicialObject.Splitting.IndexSetstatement and proof · cited by 65
CategoryTheory.SimplicialObject.Splitting.IndexSet.estatement and proof · cited by 28
CategoryTheory.Limits.image.facproof · cited by 27
CategoryTheory.SimplicialObject.Splitting.IndexSet.pullstatement · cited by 7

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀'proof · cited by 1
CategoryTheory.SimplicialObject.Splitting.IndexSet.fac_pull_assocproof · cited by 0