Theorems · Definition · algebraic topology

Path.Homotopic.Quotient.map

{X : Type u} →
  {Y : Type v} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        {x₀ x₁ : X} → Path.Homotopic.Quotient x₀ x₁ → (f : C(X, Y)) → Path.Homotopic.Quotient (f x₀) (f x₁)

The image of a path homotopy class P₀ under a map f. This is Path.map descended to the quotient.

Defined in

Mathlib.Topology.Homotopy.Path

Cited by

19 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace