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Theorems · Theorem · category theory

SSet.quasicategory_iff_hasLiftingProperty

∀ (S : SSet) {X : SSet} (t : CategoryTheory.Limits.IsTerminal X),
  S.Quasicategory ↔
    ∀ {n : ℕ} {i : Fin (n + 1)}, 0 < i → i < Fin.last n → CategoryTheory.HasLiftingProperty (SSet.horn n i).ι (t.from S)
Defined in
Mathlib.AlgebraicTopology.Quasicategory.Basic
Cited by
1 results in Mathlib
Foundations
Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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SSet.quasicategory_iff_innerFibration · cited by 2SSet.quasicategory_iff_in…CategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.stdSimplex · cited by 499SSet.stdSimplexSSet.Subcomplex.toSSet · cited by 315Subcomplex.toSSetSSet.horn · cited by 162SSet.hornCategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalSSet.Subcomplex.ι · cited by 136Subcomplex.ιCategoryTheory.HasLiftingProperty · cited by 50CategoryTheory.HasLifting…SSet.Quasicategory · cited by 14SSet.QuasicategorySSet.Quasicategory.hasLiftingProperty · cited by 2Quasicategory.hasLiftingP…SSet.quasicategory_of_hasLiftingProperty · cited by 2SSet.quasicategory_of_has…SSet.quasicategory_iff_hasLif…CITED BYCITES

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