Theorems · Inductive type · category theory
SSet.Quasicategory
SSet → Prop
A simplicial set S is a quasicategory if it satisfies the following horn-filling condition:
for every n : ℕ and 0 < i < n,
every map of simplicial sets σ₀ : Λ[n, i] → S can be extended to a map σ : Δ[n] → S.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SSetstatement · cited by 1,283
Cited by18
Results whose statement or proof uses this declaration.
- SSet.Quasicategory.hasLiftingPropertystatement and proof · cited by 2
- SSet.quasicategory_of_hasLiftingPropertystatement · cited by 2
- SSet.quasicategory_iff_innerFibrationstatement · cited by 2
- SSet.Quasicategory.hornFillingstatement and proof · cited by 1
- SSet.Quasicategory.hornFilling'statement and proof · cited by 1
- SSet.quasicategory_iff_hasLiftingPropertystatement and proof · cited by 1
- SSet.quasicategory_of_fillerstatement · cited by 1
- SSet.quasicategory_of_innerFibrationstatement and proof · cited by 1
- SSet.quasicategory_of_innerFibration_quasicategorystatement · cited by 0
- SSet.QCat.forgetEnrichment.equivstatement · cited by 0
- SSet.Quasicategory.casesOnstatement and proof · cited by 0
- SSet.Quasicategory.from_innerFibrationsstatement and proof · cited by 0