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