Theorems · Definition · algebraic topology
Path.Homotopic.Quotient
{X : Type u} → [TopologicalSpace X] → X → X → Type uThe quotient on Path x₀ x₁ by the equivalence relation Path.Homotopic.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 131 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.
Cites2
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
- Path.Homotopic.setoidproof · cited by 14
Cited by72
Results whose statement or proof uses this declaration.
- Path.Homotopic.Quotient.mkstatement · cited by 28
- IsCoveringMap.monodromystatement and proof · cited by 27
- Path.Homotopic.Quotient.mapstatement and proof · cited by 19
- Path.Homotopic.Quotient.caststatement and proof · cited by 16
- Path.Homotopic.Quotient.transstatement and proof · cited by 12
- Path.Homotopic.Quotient.reflstatement · cited by 9
- Path.Homotopic.Quotient.indstatement and proof · cited by 8
- Path.Homotopic.prodstatement and proof · cited by 6
- Path.Homotopic.pistatement and proof · cited by 5
- Path.Homotopic.Quotient.symmstatement and proof · cited by 5
- Path.Homotopic.Quotient.cast_rfl_rflstatement and proof · cited by 3
- Path.Homotopic.Quotient.eqstatement · cited by 3