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Theorems · Theorem · algebraic topology

SSet.horn.multicoequalizerDiagram

∀ {n : ℕ} (i : Fin (n + 1)),
  (SSet.horn n i).MulticoequalizerDiagram (fun j => SSet.stdSimplex.face {↑j}ᶜ) fun j k =>
    SSet.stdSimplex.face {↑j, ↑k}ᶜ

The multicoequalizer diagram which expresses Λ[n, i] as a gluing of all 1-codimensional faces of the standard simplex but one along suitable 2-codimensional faces.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.HornColimits
Cited by
16 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

SSet.horn₃₁.desc.multicofork · cited by 10desc.multicoforkSSet.horn₃₂.desc.multicofork · cited by 10desc.multicoforkSSet.horn.isColimit · cited by 8horn.isColimitSSet.horn.hom_ext' · cited by 2horn.hom_ext'SSet.horn₃₁.desc.multicofork_π_three · cited by 1desc.multicofork_π_threeSSet.horn₃₁.desc.multicofork_π_two · cited by 1desc.multicofork_π_twoSSet.horn₃₁.desc.multicofork_π_zero · cited by 1desc.multicofork_π_zeroSSet.horn₃₂.desc.multicofork_π_one · cited by 1desc.multicofork_π_oneSSet.horn₃₂.desc.multicofork_π_three · cited by 1desc.multicofork_π_threeSSet.horn₃₂.desc.multicofork_π_zero · cited by 1desc.multicofork_π_zeroSSet.horn.IsCompatible.exists_desc · cited by 1IsCompatible.exists_descSSet.horn₃₁.desc.multicofork_pt · cited by 0desc.multicofork_ptSSet.horn₃₁.desc.multicofork_π_three_assoc · cited by 0desc.multicofork_π_three_…SSet.horn₃₁.desc.multicofork_π_two_assoc · cited by 0desc.multicofork_π_two_as…SSet.horn₃₁.desc.multicofork_π_zero_assoc · cited by 0desc.multicofork_π_zero_a…Set · cited by 53352SetCategoryTheory.Functor.obj · cited by 19642Functor.objFinset · cited by 13712FinsetOpposite · cited by 8081OppositeSet.Elem · cited by 7166Set.ElemCompl.compl · cited by 2925Compl.compliSup · cited by 2415iSupSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetFinset.ext · cited by 565Finset.extSSet.stdSimplex · cited by 499SSet.stdSimplexSSet.Subcomplex · cited by 461SSet.SubcomplexSSet.horn · cited by 162SSet.hornSSet.stdSimplex.face · cited by 77stdSimplex.faceSSet.horn_eq_iSup · cited by 9SSet.horn_eq_iSuphorn.multicoequalizerDiagramCITED BYCITES

Cites18

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

Cited by19

Results whose statement or proof uses this declaration.