Theorems · Definition · algebraic topology
SimplexCategory.toTopHomeo
(n : SimplexCategory) → ↑(SSet.toTop.obj (SSet.stdSimplex.obj n)) ≃ₜ ↑(stdSimplex ℝ (Fin (n.len + 1)))
The homeomorphism between the topological realization of a standard simplex
in SSet and the corresponding topological standard simplex.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- Set.Elemstatement · cited by 7,166
- TopCat.carrierstatement · cited by 3,184
- SimplexCategorystatement and proof · cited by 2,204
- TopCatstatement · cited by 1,889
- SSetstatement · cited by 1,283
- Homeomorphstatement · cited by 725
- SimplexCategory.lenstatement · cited by 542
- SSet.stdSimplexstatement · cited by 499
Cited by7
Results whose statement or proof uses this declaration.
- SimplexCategory.toTopHomeo_naturality_applystatement · cited by 2
- SimplexCategory.toTopHomeo_naturalitystatement and proof · cited by 1
- SimplexCategory.toTopHomeo_symm_naturalitystatement · cited by 1
- SSet.stdSimplex.δ_one_toSSetObjIproof · cited by 1
- SSet.stdSimplex.δ_zero_toSSetObjIproof · cited by 1
- SSet.stdSimplex.toTopObjIsoIproof · cited by 0
- SimplexCategory.toTopHomeo_symm_naturality_applystatement · cited by 0