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isomorphism of truncations of h-groups

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Ulrik Buchholtz 2017-07-07 23:04:27 +01:00
parent b8bb1ca67d
commit bb3995c573
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move_to_lib.hlean
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@ -439,6 +439,13 @@ namespace group
definition isomorphism_of_is_contr {G H : Group} (hG : is_contr G) (hH : is_contr H) : G ≃g H := definition isomorphism_of_is_contr {G H : Group} (hG : is_contr G) (hH : is_contr H) : G ≃g H :=
trivial_group_of_is_contr G ⬝g (trivial_group_of_is_contr H)⁻¹ᵍ trivial_group_of_is_contr G ⬝g (trivial_group_of_is_contr H)⁻¹ᵍ
definition trunc_isomorphism_of_equiv {A B : Type} [inf_group A] [inf_group B] (f : A ≃ B)
(h : is_mul_hom f) : Group.mk (trunc 0 A) (trunc_group A) ≃g Group.mk (trunc 0 B) (trunc_group B) :=
begin
apply isomorphism_of_equiv (equiv.mk (trunc_functor 0 f) (is_equiv_trunc_functor 0 f)), intros x x',
induction x with a, induction x' with a', apply ap tr, exact h a a'
end
end group open group end group open group
namespace fiber namespace fiber