Theorems · Definition · algebraic topology
TopCat.toSSetIsoConst
(X : TopCat) → [TotallyDisconnectedSpace ↑X] → TopCat.toSSet.obj X ≅ (CategoryTheory.Functor.const SimplexCategoryᵒᵖ).obj ↑X
The singular simplicial set of a totally disconnected space is the constant simplicial set.
- Defined in
- Mathlib.AlgebraicTopology.SingularSet
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TotallyDisconnectedSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Set.Elemproof · cited by 7,166
- CategoryTheory.Isostatement · cited by 3,963
- Equiv.symmproof · cited by 3,681
- TopCat.carrierstatement and proof · cited by 3,184
- Opposite.unopproof · cited by 2,231
- SimplexCategorystatement and proof · cited by 2,204
- TopCatstatement and proof · cited by 1,889
- SSetstatement · cited by 1,283
Cited by1
Results whose statement or proof uses this declaration.