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lines changed Original file line number Diff line number Diff line change @@ -180,13 +180,6 @@ Additions to existing modules
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rawModule : RawModule R c ℓ
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```
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- * In ` Algebra.Morphism.Structures ` :
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- ``` agda
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- IsSemigroupHomomorphism : (A → B) → Set _
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- IsSemigroupMonomorphism : (A → B) → Set _
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- IsSemigroupIsomorphism : (A → B) → Set _
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- ```
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-
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* In ` Algebra.Properties.Group ` :
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``` agda
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isQuasigroup : IsQuasigroup _∙_ _\\_ _//_
Original file line number Diff line number Diff line change @@ -68,15 +68,6 @@ module MagmaMorphisms (M₁ : RawMagma a ℓ₁) (M₂ : RawMagma b ℓ₂) wher
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; surjective = surjective
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}
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- IsSemigroupHomomorphism : (⟦_⟧ : A → B) → Set (a ⊔ ℓ₁ ⊔ ℓ₂)
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- IsSemigroupHomomorphism = IsMagmaHomomorphism
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-
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- IsSemigroupMonomorphism : (⟦_⟧ : A → B) → Set (a ⊔ ℓ₁ ⊔ ℓ₂)
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- IsSemigroupMonomorphism = IsMagmaMonomorphism
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-
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- IsSemigroupIsomorphism : (⟦_⟧ : A → B) → Set (a ⊔ b ⊔ ℓ₁ ⊔ ℓ₂)
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- IsSemigroupIsomorphism = IsMagmaIsomorphism
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-
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------------------------------------------------------------------------
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-- Morphisms over monoid-like structures
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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module Function.Endomorphism.Propositional {a} (A : Set a) where
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- open import Algebra
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- open import Algebra.Structures
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+ open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
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+ open import Algebra.Core
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+ open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
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open import Algebra.Morphism
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- open Definitions
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+ using (module Definitions ; IsMagmaHomomorphism; IsMonoidHomomorphism)
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+ open Definitions using (Homomorphic₂)
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open import Data.Nat.Base using (ℕ; _+_; zero; suc; +-rawMagma; +-0-rawMonoid)
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open import Data.Nat.Properties using (+-0-monoid; +-semigroup)
@@ -92,7 +94,7 @@ private
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------------------------------------------------------------------------
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-- Homomorphism
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- ^-isSemigroupMorphism : ∀ f → IsSemigroupHomomorphism +-rawMagma ∘-rawMagma (f ^_)
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+ ^-isSemigroupMorphism : ∀ f → IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
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^-isSemigroupMorphism f = record
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{ isRelHomomorphism = record { cong = cong (f ^_) }
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; homo = ^-homo f
Original file line number Diff line number Diff line change @@ -15,7 +15,7 @@ open import Agda.Builtin.Equality
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open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
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open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
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open import Algebra.Morphism
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- using (module Definitions ; IsSemigroupHomomorphism ; IsMonoidHomomorphism)
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+ using (module Definitions ; IsMagmaHomomorphism ; IsMonoidHomomorphism)
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open Definitions using (Homomorphic₂)
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open import Data.Nat.Base using (ℕ; _+_; +-rawMagma; +-0-rawMonoid)
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open ℕ
@@ -98,7 +98,7 @@ private
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------------------------------------------------------------------------
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-- Homomorphism
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- ^-isSemigroupHomomorphism : ∀ f → IsSemigroupHomomorphism +-rawMagma ∘-rawMagma (f ^_)
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+ ^-isSemigroupHomomorphism : ∀ f → IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
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^-isSemigroupHomomorphism f = record
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{ isRelHomomorphism = record { cong = ^-cong₂ f }
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; homo = ^-homo f
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