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small changes to spectrum

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This commit is contained in:
Floris van Doorn 2017-06-07 00:54:52 -04:00
parent 74955d5a75
commit 3881982774
2 changed files with 6 additions and 5 deletions
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2
homotopy/smash.hlean
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@ -5,7 +5,7 @@ import homotopy.smash types.pointed2 .pushout homotopy.red_susp
open bool pointed eq equiv is_equiv sum bool prod unit circle cofiber prod.ops wedge is_trunc open bool pointed eq equiv is_equiv sum bool prod unit circle cofiber prod.ops wedge is_trunc
function red_susp unit function red_susp unit
/- To prove: Σ(X × Y) ≃ ΣX ∨ ΣY ∨ Σ(X ∧ Y) (?) (notation means suspension, wedge, smash) -/ /- To prove: Σ(X × Y) ≃ ΣX ∨ ΣY ∨ Σ(X ∧ Y) (notation means suspension, wedge, smash) -/
/- To prove: Σ(X ∧ Y) ≃ X ★ Y (?) (notation means suspension, smash, join) -/ /- To prove: Σ(X ∧ Y) ≃ X ★ Y (?) (notation means suspension, smash, join) -/

9
homotopy/spectrum.hlean
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@ -397,16 +397,16 @@ namespace spectrum
spectrify_type X n ≃* Ω (spectrify_type X (S n)) := spectrify_type X n ≃* Ω (spectrify_type X (S n)) :=
begin begin
refine !pshift_equiv ⬝e* _, refine !pshift_equiv ⬝e* _,
refine _ ⬝e* !pseq_colim_loop⁻¹ᵉ*, transitivity pseq_colim (λk, spectrify_type_fun' X (succ k) (S n +' k)),
transitivity pseq_colim (λk, spectrify_type_fun' X (succ k) (S n +' k)), rotate 1,
refine pseq_colim_equiv_constant (λn, !ap1_pcompose⁻¹*),
fapply pseq_colim_pequiv, fapply pseq_colim_pequiv,
{ intro n, apply loopn_pequiv_loopn, apply pequiv_ap X, apply succ_str.add_succ }, { intro n, apply loopn_pequiv_loopn, apply pequiv_ap X, apply succ_str.add_succ },
{ intro k, apply to_homotopy, { intro k, apply to_homotopy,
refine !passoc⁻¹* ⬝* _, refine pwhisker_right _ (loopn_succ_in_inv_natural (succ k) _) ⬝* _, refine !passoc⁻¹* ⬝* _, refine pwhisker_right _ (loopn_succ_in_inv_natural (succ k) _) ⬝* _,
refine !passoc ⬝* _ ⬝* !passoc⁻¹*, apply pwhisker_left, refine !passoc ⬝* _ ⬝* !passoc⁻¹*, apply pwhisker_left,
refine !apn_pcompose⁻¹* ⬝* _ ⬝* !apn_pcompose, apply apn_phomotopy, refine !apn_pcompose⁻¹* ⬝* _ ⬝* !apn_pcompose, apply apn_phomotopy,
exact !glue_ptransport⁻¹* } exact !glue_ptransport⁻¹* },
refine _ ⬝e* !pseq_colim_loop⁻¹ᵉ*,
refine pseq_colim_equiv_constant (λn, !ap1_pcompose⁻¹*),
end end
definition spectrify [constructor] {N : succ_str} (X : gen_prespectrum N) : gen_spectrum N := definition spectrify [constructor] {N : succ_str} (X : gen_prespectrum N) : gen_spectrum N :=
@ -431,6 +431,7 @@ namespace spectrum
--pshift_equiv_pinclusion (spectrify_type_fun X n) 0 --pshift_equiv_pinclusion (spectrify_type_fun X n) 0
refine _ ⬝v* _, refine _ ⬝v* _,
rotate 1, exact pshift_equiv_pinclusion (spectrify_type_fun X n) 0, rotate 1, exact pshift_equiv_pinclusion (spectrify_type_fun X n) 0,
-- refine !passoc⁻¹* ⬝* pwhisker_left _ _ ⬝* _,
exact sorry exact sorry
} }
end end