Theorems · Theorem · category theory
SSet.Quasicategory.hornFilling
∀ {S : SSet} [S.Quasicategory] ⦃n : ℕ⦄ ⦃i : Fin (n + 1)⦄,
0 < i →
i < Fin.last n →
∀ (σ₀ : (SSet.horn n i).toSSet ⟶ S), ∃ σ, σ₀ = CategoryTheory.CategoryStruct.comp (SSet.horn n i).ι σ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SSet.Quasicategory
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · 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
- SSet.Subcomplex.toSSetstatement and proof · cited by 315
- SSet.hornstatement and proof · cited by 162
- SSet.Subcomplex.ιstatement and proof · cited by 136
- SSet.Quasicategorystatement and proof · cited by 14
- SSet.Quasicategory.hornFilling'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SSet.Quasicategory.hasLiftingPropertyproof · cited by 2