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useless commit

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Egbert Rijke 2017-02-08 12:26:23 -05:00
parent c0b7740f13
commit e3f1d64330
1 changed files with 14 additions and 0 deletions
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14
algebra/exact_couple.hlean
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@ -35,6 +35,8 @@ structure hom_SES {A B C A' B' C' : AbGroup} (ses : SES A B C) (ses' : SES A' B'
-- fapply ab_group_first_iso_thm B C (SES.g ses),
-- end
-- definition pre_right_extend_SES (to separate the following definition and replace C with B/A)
definition right_extend_SES {A B C A' B' C' : AbGroup}
(ses : SES A B C) (ses' : SES A' B' C')
(hA : A →g A') (hB : B →g B') (htpy1 : hB ∘g (SES.f ses) ~ (SES.f ses') ∘g hA) : C →g C' :=
@ -51,6 +53,18 @@ definition right_extend_SES {A B C A' B' C' : AbGroup}
fapply is_exact.im_in_ker (SES.ex ses') (hA a),
end
definition right_extend_hom_SES {A B C A' B' C' : AbGroup}
(ses : SES A B C) (ses' : SES A' B' C')
(hA : A →g A') (hB : B →g B') (htpy1 : hB ∘g (SES.f ses) ~ (SES.f ses') ∘g hA) : hom_SES ses ses' :=
begin
fapply hom_SES.mk,
exact hA,
exact hB,
exact right_extend_SES ses ses' hA hB htpy1,
exact htpy1,
exact sorry -- fapply quotient_group_compute,
end
definition is_differential {B : AbGroup} (d : B →g B) := Π(b:B), d (d b) = 1
definition image_subgroup_of_diff {B : AbGroup} (d : B →g B) (H : is_differential d) : subgroup_rel (ab_kernel d) :=