Theorems · Definition · algebraic topology
SSet.stdSimplex.isoNerve
(n : ℕ) → SSet.stdSimplex.obj { len := n } ≅ CategoryTheory.nerve (ULift.{u, 0} (Fin (n + 1)))The standard simplex identifies to the nerve to the preordered type
ULift (Fin (n + 1)).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Isostatement · cited by 3,963
- Opposite.unopproof · cited by 2,231
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- Equiv.transproof · cited by 337
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.nervestatement and proof · cited by 68
- Monotone.functorproof · cited by 66
Cited by3
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.mem_nonDegenerate_iff_strictMonoproof · cited by 2
- SSet.stdSimplex.isoNerve_hom_app_applystatement · cited by 0
- SSet.stdSimplex.isoNerve_inv_app_applystatement · cited by 0