Theorems · Definition · algebraic topology

Path.Homotopic.Quotient.trans

{X : Type u} →
  [inst : TopologicalSpace X] →
    {x₀ x₁ x₂ : X} → Path.Homotopic.Quotient x₀ x₁ → Path.Homotopic.Quotient x₁ x₂ → Path.Homotopic.Quotient x₀ x₂

The composition of path homotopy classes. This is Path.trans descended to the quotient.

Defined in: Mathlib.Topology.Homotopy.Path
Cited by: 12 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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Cites6

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
Pathproof · cited by 318
Path.Homotopic.Quotientstatement and proof · cited by 55
Path.transproof · cited by 54
Quotient.map₂proof · cited by 3
Path.Homotopic.hcompproof · cited by 1

Cited by12

Results whose statement or proof uses this declaration.

Path.Homotopic.Quotient.mk_transstatement · cited by 1
Path.Homotopic.Quotient.symm_transstatement · cited by 1
Path.Homotopic.Quotient.trans_assocstatement · cited by 1
Path.Homotopic.Quotient.trans_reflstatement · cited by 1
simply_connected_iff_loops_nullhomotopicproof · cited by 1
Path.Homotopic.comp_pi_eq_pi_compstatement and proof · cited by 0
Path.Homotopic.comp_prod_eq_prod_compstatement · cited by 0
FundamentalGroupoid.comp_eqstatement · cited by 0
IsCoveringMap.monodromy_trans_applystatement · cited by 0
Path.Homotopic.Quotient.refl_transstatement · cited by 0
Path.Homotopic.Quotient.trans_symmstatement · cited by 0
FundamentalGroup.mul_defstatement · cited by 0