Theorems · Theorem · algebraic topology
SSet.Subcomplex.isIso_toOfSimplex_iff
∀ {X : SSet} {n : ℕ} (x : X.obj (Opposite.op { len := n })),
CategoryTheory.IsIso (SSet.Subcomplex.toOfSimplex x) ↔ CategoryTheory.Mono (SSet.yonedaEquiv.symm x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- Equiv.symmstatement and proof · cited by 3,681
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- SSet.stdSimplexstatement and proof · cited by 499
- SSet.Subcomplex.toSSetstatement · cited by 315
Cited by1
Results whose statement or proof uses this declaration.
- SSet.Nonsingular.isIso_toOfSimplexproof · cited by 0