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Add pwedge_pequiv and plift_pwedge.

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favonia 2017-06-08 14:11:02 -06:00
parent 85c0ae53a6
commit 4165f9a613
1 changed files with 12 additions and 1 deletions
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13
homotopy/wedge.hlean
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@ -2,7 +2,7 @@
import homotopy.wedge
open wedge pushout eq prod sum pointed equiv is_equiv unit
open wedge pushout eq prod sum pointed equiv is_equiv unit lift
namespace wedge
@ -38,4 +38,15 @@ namespace wedge
-- TODO: wedge is associative
definition pwedge_pequiv [constructor] {A A' B B' : Type*} (a : A ≃* A') (b : B ≃* B') : A ∨ B ≃* A' ∨ B' :=
begin
fapply pequiv_of_equiv,
exact pushout.equiv !pconst !pconst !pconst !pconst !pequiv.refl a b (λdummy, respect_pt a) (λdummy, respect_pt b),
exact ap pushout.inl (respect_pt a)
end
definition plift_pwedge.{u v} (A B : Type*) : plift.{u v} (A ∨ B) ≃* plift.{u v} A ∨ plift.{u v} B :=
calc plift.{u v} (A ∨ B) ≃* A ∨ B : by exact !pequiv_plift⁻¹ᵉ*
... ≃* plift.{u v} A ∨ plift.{u v} B : by exact pwedge_pequiv !pequiv_plift !pequiv_plift
end wedge