Theorems · Theorem · algebraic topology
ContinuousMap.HomotopyEquiv.left_inv
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(self : ContinuousMap.HomotopyEquiv X Y), (self.invFun.comp self.toFun).Homotopic (ContinuousMap.id X)- Defined in
- Mathlib.Topology.Homotopy.Equiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- ContinuousMap.compstatement · cited by 181
- ContinuousMap.idstatement · cited by 73
- ContinuousMap.Homotopicstatement · cited by 24
- ContinuousMap.HomotopyEquivstatement and proof · cited by 23
- ContinuousMap.HomotopyEquiv.toFunstatement · cited by 12
- ContinuousMap.HomotopyEquiv.invFunstatement · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMap.HomotopyEquiv.symmproof · cited by 8
- id_nullhomotopicproof · cited by 2
- FundamentalGroupoidFunctor.equivOfHomotopyEquivproof · cited by 1