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https://github.com/Smaug123/agdaproofs
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19 lines
860 B
Agda
19 lines
860 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Setoids.Setoids
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import Groups.Definition
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module Groups.Actions.Definition where
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record GroupAction {m n o p : _} {A : Set m} {S : Setoid {m} {o} A} {_·_ : A → A → A} {B : Set n} (G : Group S _·_) (X : Setoid {n} {p} B) : Set (m ⊔ n ⊔ o ⊔ p) where
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open Group G
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open Setoid S renaming (_∼_ to _∼G_)
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open Setoid X renaming (_∼_ to _∼X_)
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field
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action : A → B → B
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actionWellDefined1 : {g h : A} → {x : B} → (g ∼G h) → action g x ∼X action h x
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actionWellDefined2 : {g : A} → {x y : B} → (x ∼X y) → action g x ∼X action g y
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identityAction : {x : B} → action 0G x ∼X x
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associativeAction : {x : B} → {g h : A} → action (g · h) x ∼X action g (action h x)
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