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redefine sid

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Egbert Rijke 2017-07-01 14:46:38 +01:00
parent aa1d1bd333
commit 8561c20aa6
1 changed files with 12 additions and 9 deletions
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homotopy/spectrum.hlean
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@ -1,11 +1,12 @@
/- /-
Copyright (c) 2016 Michael Shulman. All rights reserved. Copyright (c) 2016 Michael Shulman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Shulman, Floris van Doorn, Stefano Piceghello, Yuri Sulyma Authors: Michael Shulman, Floris van Doorn, Egbert Rijke, Stefano Piceghello, Yuri Sulyma
-/ -/
import homotopy.LES_of_homotopy_groups .splice ..colim types.pointed2 .EM ..pointed_pi .smash_adjoint ..algebra.seq_colim .fwedge import homotopy.LES_of_homotopy_groups .splice ..colim types.pointed2 .EM ..pointed_pi .smash_adjoint ..algebra.seq_colim .fwedge .pointed_cubes
open eq nat int susp pointed pmap sigma is_equiv equiv fiber algebra trunc trunc_index pi group open eq nat int susp pointed pmap sigma is_equiv equiv fiber algebra trunc trunc_index pi group
seq_colim succ_str EM EM.ops function seq_colim succ_str EM EM.ops function
@ -148,15 +149,17 @@ namespace spectrum
-- A version of 'glue_square' in the spectrum case that uses 'equiv_glue' -- A version of 'glue_square' in the spectrum case that uses 'equiv_glue'
definition sglue_square {N : succ_str} {E F : gen_spectrum N} (f : E →ₛ F) (n : N) definition sglue_square {N : succ_str} {E F : gen_spectrum N} (f : E →ₛ F) (n : N)
: equiv_glue F n ∘* f n ~* Ω→ (f (S n)) ∘* equiv_glue E n : psquare (f n) (Ω→ (f (S n))) (equiv_glue E n) (equiv_glue F n) :=
-- I guess this manual eta-expansion is necessary because structures lack definitional eta? glue_square f n
:= phomotopy.mk (glue_square f n) (to_homotopy_pt (glue_square f n))
definition sid [constructor] [refl] {N : succ_str} (E : gen_prespectrum N) : E →ₛ E := definition sid [constructor] [refl] {N : succ_str} (E : gen_prespectrum N) : E →ₛ E :=
smap.mk (λn, pid (E n)) smap.mk (λ n, pid (E n)) (λ n, psquare_of_phtpy_bot (ap1_pid) (psquare_of_pid_top_bot (phomotopy.rfl)))
(λn, calc glue E n ∘* pid (E n) ~* glue E n : pcompose_pid
... ~* pid (Ω(E (S n))) ∘* glue E n : pid_pcompose print sid
... ~* Ω→(pid (E (S n))) ∘* glue E n : pwhisker_right (glue E n) ap1_pid⁻¹*) -- smap.mk (λn, pid (E n))
-- (λn, calc glue E n ∘* pid (E n) ~* glue E n : pcompose_pid
-- ... ~* pid (Ω(E (S n))) ∘* glue E n : pid_pcompose
-- ... ~* Ω→(pid (E (S n))) ∘* glue E n : pwhisker_right (glue E n) ap1_pid⁻¹*)
definition scompose [trans] {N : succ_str} {X Y Z : gen_prespectrum N} definition scompose [trans] {N : succ_str} {X Y Z : gen_prespectrum N}
(g : Y →ₛ Z) (f : X →ₛ Y) : X →ₛ Z := (g : Y →ₛ Z) (f : X →ₛ Y) : X →ₛ Z :=