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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -180,13 +180,6 @@ Additions to existing modules
180180 rawModule : RawModule R c ℓ
181181 ```
182182
183- * In ` Algebra.Morphism.Structures ` :
184- ``` agda
185- IsSemigroupHomomorphism : (A → B) → Set _
186- IsSemigroupMonomorphism : (A → B) → Set _
187- IsSemigroupIsomorphism : (A → B) → Set _
188- ```
189-
190183 * In ` Algebra.Properties.Group ` :
191184 ``` agda
192185 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
6868 ; surjective = surjective
6969 }
7070
71- IsSemigroupHomomorphism : (⟦_⟧ : A → B) → Set (a ⊔ ℓ₁ ⊔ ℓ₂)
72- IsSemigroupHomomorphism = IsMagmaHomomorphism
73-
74- IsSemigroupMonomorphism : (⟦_⟧ : A → B) → Set (a ⊔ ℓ₁ ⊔ ℓ₂)
75- IsSemigroupMonomorphism = IsMagmaMonomorphism
76-
77- IsSemigroupIsomorphism : (⟦_⟧ : A → B) → Set (a ⊔ b ⊔ ℓ₁ ⊔ ℓ₂)
78- IsSemigroupIsomorphism = IsMagmaIsomorphism
79-
8071------------------------------------------------------------------------
8172-- Morphisms over monoid-like structures
8273------------------------------------------------------------------------
Original file line number Diff line number Diff line change 77{-# OPTIONS --cubical-compatible --safe #-}
88module Function.Endomorphism.Propositional {a} (A : Set a) where
99
10- open import Algebra
11- open import Algebra.Structures
10+ open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
11+ open import Algebra.Core
12+ open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
1213open import Algebra.Morphism
13- open Definitions
14+ using (module Definitions ; IsMagmaHomomorphism; IsMonoidHomomorphism)
15+ open Definitions using (Homomorphic₂)
1416
1517open import Data.Nat.Base using (ℕ; _+_; zero; suc; +-rawMagma; +-0-rawMonoid)
1618open import Data.Nat.Properties using (+-0-monoid; +-semigroup)
@@ -92,7 +94,7 @@ private
9294------------------------------------------------------------------------
9395-- Homomorphism
9496
95- ^-isSemigroupMorphism : ∀ f → IsSemigroupHomomorphism +-rawMagma ∘-rawMagma (f ^_)
97+ ^-isSemigroupMorphism : ∀ f → IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
9698^-isSemigroupMorphism f = record
9799 { isRelHomomorphism = record { cong = cong (f ^_) }
98100 ; homo = ^-homo f
Original file line number Diff line number Diff line change @@ -15,7 +15,7 @@ open import Agda.Builtin.Equality
1515open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
1616open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
1717open import Algebra.Morphism
18- using (module Definitions ; IsSemigroupHomomorphism ; IsMonoidHomomorphism)
18+ using (module Definitions ; IsMagmaHomomorphism ; IsMonoidHomomorphism)
1919open Definitions using (Homomorphic₂)
2020open import Data.Nat.Base using (ℕ; _+_; +-rawMagma; +-0-rawMonoid)
2121open ℕ
@@ -98,7 +98,7 @@ private
9898------------------------------------------------------------------------
9999-- Homomorphism
100100
101- ^-isSemigroupHomomorphism : ∀ f → IsSemigroupHomomorphism +-rawMagma ∘-rawMagma (f ^_)
101+ ^-isSemigroupHomomorphism : ∀ f → IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
102102^-isSemigroupHomomorphism f = record
103103 { isRelHomomorphism = record { cong = ^-cong₂ f }
104104 ; homo = ^-homo f
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