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redefine sid

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This commit is contained in:
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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21
homotopy/spectrum.hlean
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@ -1,11 +1,12 @@
/-
Copyright (c) 2016 Michael Shulman. All rights reserved.
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
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'
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
-- I guess this manual eta-expansion is necessary because structures lack definitional eta?
:= phomotopy.mk (glue_square f n) (to_homotopy_pt (glue_square f n))
: psquare (f n) (Ω→ (f (S n))) (equiv_glue E n) (equiv_glue F n) :=
glue_square f n
definition sid [constructor] [refl] {N : succ_str} (E : gen_prespectrum N) : E →ₛ E :=
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*)
smap.mk (λ n, pid (E n)) (λ n, psquare_of_phtpy_bot (ap1_pid) (psquare_of_pid_top_bot (phomotopy.rfl)))
print sid
-- 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}
(g : Y →ₛ Z) (f : X →ₛ Y) : X →ₛ Z :=