Theorems · Definition · algebraic topology
Path.Homotopy.eval
{X : Type u} →
[inst : TopologicalSpace X] → {x₀ x₁ : X} → {p₀ p₁ : Path x₀ x₁} → p₀.Homotopy p₁ → ↑unitInterval → Path x₀ x₁Evaluating a path homotopy at an intermediate point, giving us a Path.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
- Path.Homotopystatement and proof · cited by 21
- ContinuousMap.HomotopyWith.toHomotopyproof · cited by 17
- ContinuousMap.Homotopy.curryproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- Path.Homotopy.hcompproof · cited by 3
- Path.Homotopy.eval_applystatement and proof · cited by 2
- Path.Homotopy.eval_onestatement · cited by 0
- Path.Homotopy.eval_zerostatement · cited by 0
- Path.Homotopy.hcomp_applystatement and proof · cited by 0
- Path.Homotopy.hcomp_halfproof · cited by 0