lean2/hott/homotopy/smash.hlean
2016-02-09 09:57:33 -08:00

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/-
Copyright (c) 2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
The Smash Product of Types
-/
import hit.pushout .wedge .cofiber .susp .sphere
open eq pushout prod pointed Pointed
definition product_of_wedge (A B : Type*) : Wedge A B →* A ×* B :=
begin
fconstructor,
intro x, induction x with [a, b], exact (a, point B), exact (point A, b),
do 2 reflexivity
end
definition Smash (A B : Type*) := Cofiber (product_of_wedge A B)
open sphere susp
namespace smash
definition susp_equiv_circle_smash (X : Type*) : Susp X ≃* Smash (Sphere 1) X :=
sorry
end smash