Theorems · Theorem · algebraic topology
SSet.nonDegenerate_iff_of_mono
∀ {X : SSet} {n : ℕ} {Y : SSet} (f : X ⟶ Y) [CategoryTheory.Mono f] (x : X.obj (Opposite.op { len := n })),
(CategoryTheory.ConcreteCategory.hom (f.app (Opposite.op { len := n }))) x ∈ Y.nonDegenerate n ↔ x ∈ X.nonDegenerate n- Cited by
- 6 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Mono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Monostatement and proof · cited by 893
- SSet.nonDegeneratestatement · cited by 106
Cited by6
Results whose statement or proof uses this declaration.
- SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquivproof · cited by 3
- SSet.stdSimplex.mem_nonDegenerate_iff_strictMonoproof · cited by 2
- SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquivproof · cited by 1
- SSet.Nonsingular.of_monoproof · cited by 1
- SSet.Subcomplex.Pairing.RankFunction.exists_or_of_range_m_Nproof · cited by 0
- SSet.nonDegenerate_δproof · cited by 0