40 lines
1.2 KiB
Text
40 lines
1.2 KiB
Text
/-
|
||
Copyright (c) 2015 Floris van Doorn. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Authors: Floris van Doorn, Egbert Rijke
|
||
|
||
Tensor group
|
||
-/
|
||
|
||
import .free_abelian_group
|
||
|
||
open eq algebra is_trunc sigma sigma.ops prod trunc function equiv
|
||
namespace group
|
||
|
||
variables {G G' : Group} {g g' h h' k : G} {A B : AbGroup}
|
||
|
||
/- Tensor group (WIP) -/
|
||
|
||
/- namespace tensor_group
|
||
variables {A B}
|
||
local abbreviation ι := @free_ab_group_inclusion
|
||
|
||
inductive tensor_rel_type : free_ab_group (Set_of_Group A ×t Set_of_Group B) → Type :=
|
||
| mul_left : Π(a₁ a₂ : A) (b : B), tensor_rel_type (ι (a₁, b) * ι (a₂, b) * (ι (a₁ * a₂, b))⁻¹)
|
||
| mul_right : Π(a : A) (b₁ b₂ : B), tensor_rel_type (ι (a, b₁) * ι (a, b₂) * (ι (a, b₁ * b₂))⁻¹)
|
||
|
||
open tensor_rel_type
|
||
|
||
definition tensor_rel' (x : free_ab_group (Set_of_Group A ×t Set_of_Group B)) : Prop :=
|
||
∥ tensor_rel_type x ∥
|
||
|
||
definition tensor_group_rel (A B : AbGroup)
|
||
: normal_subgroup_rel (free_ab_group (Set_of_Group A ×t Set_of_Group B)) :=
|
||
sorry /- relation generated by tensor_rel'-/
|
||
|
||
definition tensor_group [constructor] : AbGroup :=
|
||
quotient_ab_group (tensor_group_rel A B)
|
||
|
||
end tensor_group-/
|
||
|
||
end group
|