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25 lines
1.1 KiB
Agda
25 lines
1.1 KiB
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Setoids.Setoids
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open import Functions
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import Numbers.Naturals.Naturals
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open import Groups.Definition
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open import Groups.Homomorphisms.Definition
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open import Sets.EquivalenceRelations
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module Groups.Isomorphisms.Definition where
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record GroupIso {m n o p : _} {A : Set m} {S : Setoid {m} {o} A} {_·A_ : A → A → A} {B : Set n} {T : Setoid {n} {p} B} {_·B_ : B → B → B} (G : Group S _·A_) (H : Group T _·B_) (f : A → B) : Set (m ⊔ n ⊔ o ⊔ p) where
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open Setoid S renaming (_∼_ to _∼G_)
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open Setoid T renaming (_∼_ to _∼H_)
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field
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groupHom : GroupHom G H f
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bij : SetoidBijection S T f
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record GroupsIsomorphic {m n o p : _} {A : Set m} {S : Setoid {m} {o} A} {_·A_ : A → A → A} {B : Set n} {T : Setoid {n} {p} B} {_·B_ : B → B → B} (G : Group S _·A_) (H : Group T _·B_) : Set (m ⊔ n ⊔ o ⊔ p) where
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field
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isomorphism : A → B
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proof : GroupIso G H isomorphism
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