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Merge branch 'master' of https://github.com/cmu-phil/Spectral

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Egbert Rijke 2017-04-27 18:08:25 -04:00
commit 454401fdea
2 changed files with 36 additions and 25 deletions
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34
algebra/exact_couple.hlean
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@ -32,16 +32,36 @@ definition diff_im_in_ker {B : AbGroup} (d : B →g B) (H : is_differential d) :
definition homology {B : AbGroup} (d : B →g B) (H : is_differential d) : AbGroup := definition homology {B : AbGroup} (d : B →g B) (H : is_differential d) : AbGroup :=
@quotient_ab_group (ab_kernel d) (image_subgroup_of_diff d H) @quotient_ab_group (ab_kernel d) (image_subgroup_of_diff d H)
definition SES_of_differential {B : AbGroup} (d : B →g B) (H : is_differential d) : SES (ab_image d) (ab_kernel d) (homology d H) := definition homology_ugly {B : AbGroup} (d : B →g B) (H : is_differential d) : AbGroup :=
(quotient_ab_group (image_subgroup (ab_subgroup_of_subgroup_incl (diff_im_in_ker d H))))
definition homology_iso_ugly {B : AbGroup} (d : B →g B) (H : is_differential d) : (homology d H) ≃g (homology_ugly d H) :=
begin
-- fapply quotientgroupiso ...
exact sorry
end
definition SES_iso_C {A B C C' : AbGroup} (ses : SES A B C) (k : C ≃g C') : SES A B C' :=
begin begin
fapply SES.mk, fapply SES.mk,
exact @ab_subgroup_of_subgroup_incl B (image_subgroup d) (kernel_subgroup d) (diff_im_in_ker d H), exact SES.f ses,
exact ab_qg_map (image_subgroup_of_diff d H), exact k ∘g SES.g ses,
rexact is_embedding_ab_subgroup_of_subgroup_incl (diff_im_in_ker d H), exact SES.Hf ses,
exact is_surjective_ab_qg_map (image_subgroup_of_diff d H), fapply @is_surjective_compose _ _ _ k (SES.g ses),
exact is_surjective_of_is_equiv k,
exact SES.Hg ses,
fapply is_exact.mk, fapply is_exact.mk,
intro b, induction b, repeat exact sorry
sorry, end
definition SES_of_differential_ugly {B : AbGroup} (d : B →g B) (H : is_differential d) : SES (ab_image d) (ab_kernel d) (homology_ugly d H) :=
begin
exact SES_of_inclusion (ab_subgroup_of_subgroup_incl (diff_im_in_ker d H)) (is_embedding_ab_subgroup_of_subgroup_incl (diff_im_in_ker d H)),
end
definition SES_of_differential {B : AbGroup} (d : B →g B) (H : is_differential d) : SES (ab_image d) (ab_kernel d) (homology d H) :=
begin
exact SES_of_inclusion (ab_subgroup_of_subgroup_incl (diff_im_in_ker d H)) (is_embedding_ab_subgroup_of_subgroup_incl (diff_im_in_ker d H)),
end end
structure exact_couple (A B : AbGroup) : Type := structure exact_couple (A B : AbGroup) : Type :=

13
algebra/subgroup.hlean
View file

@ -284,17 +284,8 @@ namespace group
exact H exact H
end end
definition ab_image {G : AbGroup} {H : Group} (f : G →g H) : AbGroup := definition ab_image {G : AbGroup} {H : AbGroup} (f : G →g H) : AbGroup :=
AbGroup_of_Group (image f) ab_subgroup (image_subgroup f)
begin
intro g h,
induction g with x t, induction h with y s,
fapply subtype_eq,
induction t with p, induction s with q, induction p with g p, induction q with h q, induction p, induction q,
refine (((respect_mul f g h)⁻¹ ⬝ _) ⬝ (respect_mul f h g)),
apply (ap f),
induction G, induction struct, apply mul_comm
end
definition image_incl {G H : Group} (f : G →g H) : image f →g H := definition image_incl {G H : Group} (f : G →g H) : image f →g H :=
incl_of_subgroup (image_subgroup f) incl_of_subgroup (image_subgroup f)