Theorems · Theorem · category theory
TopCat.pathEquiv_symm_apply_hom_hom_apply
∀ {X : TopCat} {x y : ↑X} (p : Path x y) (a : ULift.{u, 0} ↑unitInterval),
(TopCat.Hom.hom (TopCat.pathEquiv.symm p).hom) a = p (TopCat.I.homeomorph a)- Defined in
- Mathlib.Topology.Homotopy.TopCat.Path
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 120 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
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Equivstatement · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Equiv.symmstatement and proof · cited by 3,681
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- Homeomorphstatement · cited by 725
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.