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couple

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Steve Awodey 2017-05-18 17:24:36 -04:00
parent f35158874a
commit 59cf3c6737
1 changed files with 21 additions and 0 deletions
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21
algebra/exact_couple.hlean
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@ -152,6 +152,27 @@ begin
... = 1 : to_respect_one, ... = 1 : to_respect_one,
end end
definition subgroup_iso_exact_at_A : ab_kernel i ≃g ab_image k :=
begin
fapply ab_subgroup_iso,
intro a,
induction EC,
induction exact_ki,
exact ker_in_im a,
intro a b, induction b with f, induction f with b p, induction p,
induction EC,
induction exact_ki,
exact im_in_ker b,
end
definition subgroup_iso_exact_at_A_triangle : ab_kernel_incl i ~ ab_image_incl k ∘g subgroup_iso_exact_at_A :=
begin
fapply ab_subgroup_iso_triangle,
intro a b, induction b with f, induction f with b p, induction p,
induction EC, induction exact_ki, exact im_in_ker b,
end
definition
definition derived_couple_j : derived_couple_A EC →g derived_couple_B EC := definition derived_couple_j : derived_couple_A EC →g derived_couple_B EC :=
begin begin
exact sorry, exact sorry,