Theorems · Theorem · algebraic topology
SSet.degenerate_iff_of_isIso
∀ {X Y : SSet} (f : X ⟶ Y) [CategoryTheory.IsIso f] {n : ℕ} (x : X.obj (Opposite.op { len := n })),
(CategoryTheory.ConcreteCategory.hom (f.app (Opposite.op { len := n }))) x ∈ Y.degenerate n ↔ x ∈ X.degenerate n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.IsIso
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- TypeCat.Funstatement · cited by 1,307
- SSetstatement and proof · cited by 1,283
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invproof · cited by 467
Cited by2
Results whose statement or proof uses this declaration.
- SSet.hasDimensionLT_of_monoproof · cited by 2
- SSet.degenerate_iff_of_monoproof · cited by 0