44 lines
1.5 KiB
Text
44 lines
1.5 KiB
Text
/-
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Copyright (c) 2015 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn, Egbert Rijke
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Constructions with groups
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-/
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import algebra.group_theory hit.set_quotient types.list types.sum .subgroup .quotient_group .product_group .free_group .free_commutative_group .direct_sum
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open eq algebra is_trunc set_quotient relation sigma sigma.ops prod prod.ops sum list trunc function
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equiv
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namespace group
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variables {G G' : Group} (H : subgroup_rel G) (N : normal_subgroup_rel G) {g g' h h' k : G}
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{A B : CommGroup}
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variables (X : Set) {l l' : list (X ⊎ X)}
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/- Tensor group (WIP) -/
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/- namespace tensor_group
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variables {A B}
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local abbreviation ι := @free_comm_group_inclusion
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inductive tensor_rel_type : free_comm_group (Set_of_Group A ×t Set_of_Group B) → Type :=
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| mul_left : Π(a₁ a₂ : A) (b : B), tensor_rel_type (ι (a₁, b) * ι (a₂, b) * (ι (a₁ * a₂, b))⁻¹)
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| mul_right : Π(a : A) (b₁ b₂ : B), tensor_rel_type (ι (a, b₁) * ι (a, b₂) * (ι (a, b₁ * b₂))⁻¹)
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open tensor_rel_type
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definition tensor_rel' (x : free_comm_group (Set_of_Group A ×t Set_of_Group B)) : Prop :=
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∥ tensor_rel_type x ∥
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definition tensor_group_rel (A B : CommGroup)
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: normal_subgroup_rel (free_comm_group (Set_of_Group A ×t Set_of_Group B)) :=
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sorry /- relation generated by tensor_rel'-/
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definition tensor_group [constructor] : CommGroup :=
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quotient_comm_group (tensor_group_rel A B)
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end tensor_group-/
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end group
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