Theorems · Definition · algebraic topology
Path.Homotopy
{X : Type u} → [inst : TopologicalSpace X] → {x₀ x₁ : X} → Path x₀ x₁ → Path x₀ x₁ → Type (max 0 u)The type of homotopies between two paths.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 115 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Pathstatement and proof · cited by 318
- Path.toContinuousMapproof · cited by 27
- ContinuousMap.HomotopyRelproof · cited by 21
Cited by44
Results whose statement or proof uses this declaration.
- Path.Homotopicproof · cited by 28
- Path.Homotopy.symmstatement and proof · cited by 8
- Path.Homotopy.evalstatement and proof · cited by 5
- Path.Homotopy.mapstatement and proof · cited by 4
- Path.Homotopy.reflTransstatement · cited by 4
- Path.Homotopy.transstatement and proof · cited by 4
- Path.Homotopy.hcompstatement and proof · cited by 3
- Path.Homotopy.caststatement and proof · cited by 2
- Path.Homotopy.eval_applystatement and proof · cited by 2
- Path.Homotopy.reflstatement · cited by 2
- Path.Homotopy.reflTransSymmstatement · cited by 2
- Path.Homotopy.symm₂statement and proof · cited by 2