Theorems · Definition · algebraic topology

Path.Homotopic.prod

{α : Type u_1} →
  {β : Type u_2} →
    [inst : TopologicalSpace α] →
      [inst_1 : TopologicalSpace β] →
        {a₁ a₂ : α} →
          {b₁ b₂ : β} →
            Path.Homotopic.Quotient a₁ a₂ → Path.Homotopic.Quotient b₁ b₂ → Path.Homotopic.Quotient (a₁, b₁) (a₂, b₂)

The product of path classes q₁ and q₂. This is Path.prod descended to the quotient.

Defined in: Mathlib.Topology.Homotopy.Product
Cited by: 6 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites4

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.Quotientstatement and proof · cited by 55
Path.prodproof · cited by 9
Quotient.map₂proof · cited by 3

Cited by7

Results whose statement or proof uses this declaration.

FundamentalGroupoidFunctor.prodToProdTopproof · cited by 7
Path.Homotopic.prod_liftstatement · cited by 2
FundamentalGroupoidFunctor.prodToProdTop_mapstatement · cited by 0
Path.Homotopic.comp_prod_eq_prod_compstatement · cited by 0
Path.Homotopic.prod_projLeft_projRightstatement and proof · cited by 0
Path.Homotopic.projLeft_prodstatement and proof · cited by 0
Path.Homotopic.projRight_prodstatement and proof · cited by 0