2016-09-09 20:43:09 +00:00
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/-
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Copyright (c) 2016 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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Reduced cohomology
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-/
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import .EM
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open spectrum int trunc pointed EM group algebra circle sphere
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definition cohomology [reducible] (X : Type*) (Y : spectrum) (n : ℤ) : Set :=
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ttrunc 0 (X →* Ω[2] (Y (n+2)))
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definition ordinary_cohomology [reducible] (X : Type*) (G : CommGroup) (n : ℤ) : Set :=
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cohomology X (EM_spectrum G) n
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definition ordinary_cohomology_Z [reducible] (X : Type*) (n : ℤ) : Set :=
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ordinary_cohomology X agℤ n
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notation `H^` n `[`:0 X:0 `, ` Y:0 `]`:0 := cohomology X Y n
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notation `H^` n `[`:0 X:0 `]`:0 := ordinary_cohomology_Z X n
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2016-09-22 20:03:08 +00:00
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check H^3[S¹*,EM_spectrum agℤ]
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check H^3[S¹*]
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