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Direct sums: preparing for vector spaces (#74)

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Patrick Stevens
2019-11-16 15:06:57 +00:00
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parent 9419587eb0
commit ff6ef4f1a1
10 changed files with 148 additions and 19 deletions
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Groups/Abelian/DirectSum.agda Normal file
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Sets.FinSet
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Groups.Abelian.Definition
module Groups.Abelian.DirectSum {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_+1_ : A → A → A} {_+2_ : B → B → B} {G1' : Group S _+1_} {G2' : Group T _+2_} (G1 : AbelianGroup G1') (G2 : AbelianGroup G2') where
open import Groups.DirectSum.Definition G1' G2'
open import Setoids.DirectSum S T
directSumAbGroup : AbelianGroup directSumGroup
AbelianGroup.commutative directSumAbGroup = directSumLift (AbelianGroup.commutative G1) (AbelianGroup.commutative G2)