Theorems · Definition · algebraic topology
SSet.horn.IsCompatible
{n : ℕ} → {X : SSet} → {i : Fin (n + 2)} → ((j : Fin (n + 2)) → j ≠ i → (SSet.stdSimplex.obj { len := n } ⟶ X)) → PropLet i : Fin (n + 2). This is the condition that a family of morphisms
Δ[n] ⟶ X for j ≠ i are the "faces" of a morphism Λ[n + 1, i] ⟶ X.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.stdSimplexstatement and proof · cited by 499
- CategoryTheory.CosimplicialObject.δproof · cited by 129
- Fin.castPredproof · cited by 89
Cited by23
Results whose statement or proof uses this declaration.
- SSet.horn.IsCompatible.liftstatement and proof · cited by 5
- SSet.horn.IsCompatible.descstatement and proof · cited by 4
- SSet.horn.IsCompatible.liftOfKanComplexstatement and proof · cited by 3
- SSet.horn.IsCompatible.exists_liftstatement and proof · cited by 3
- SSet.horn.IsCompatible.ι_descstatement and proof · cited by 2
- SSet.horn.IsCompatible.exists_lift_of_kanComplexstatement and proof · cited by 2
- SSet.horn.IsCompatible.lift_compstatement and proof · cited by 1
- SSet.horn.IsCompatible.of_homstatement · cited by 1
- SSet.horn.IsCompatible.δ_liftstatement and proof · cited by 1
- SSet.horn.IsCompatible.δ_liftOfKanComplexstatement and proof · cited by 1
- SSet.horn.IsCompatible.δ_pred_compstatement and proof · cited by 1
- SSet.horn.IsCompatible.ι_desc_assocstatement and proof · cited by 1