Theorems · Definition · algebraic topology
ContinuousMap.Homotopy.hcast
{X : TopCat} → {x₀ x₁ : ↑X} → x₀ = x₁ → (FundamentalGroupoid.fromTop x₀ ⟶ FundamentalGroupoid.fromTop x₁)Abbreviation for eqToHom that accepts points in a topological space
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- TopCat.carrierstatement and proof · cited by 3,184
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.eqToHomproof · cited by 860
- CategoryTheory.Bundled.αstatement · cited by 736
- CategoryTheory.Groupoidstatement · cited by 182
- CategoryTheory.Grpdstatement · cited by 30
- FundamentalGroupoid.fundamentalGroupoidFunctorstatement · cited by 21
- FundamentalGroupoid.fromTopstatement · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- ContinuousMap.Homotopy.eq_path_of_eq_imagestatement · cited by 2
- ContinuousMap.Homotopy.apply_one_pathstatement · cited by 1
- ContinuousMap.Homotopy.apply_zero_pathstatement · cited by 1
- ContinuousMap.Homotopy.diagonalPath'proof · cited by 1
- ContinuousMap.Homotopy.evalAt_eqstatement · cited by 1
- ContinuousMap.Homotopy.eq_diag_pathproof · cited by 0
- ContinuousMap.Homotopy.hcast_defstatement · cited by 0