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lines changed Original file line number Diff line number Diff line change @@ -15,7 +15,7 @@ module Algebra.Module.Definitions.Bi
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{a a′ b ℓb} (A : Set a) (A′ : Set a′) {B : Set b} (_≈_ : Rel B ℓb)
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where
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- open import Algebra.Module.Core
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+ open import Algebra.Module.Core using (Opₗ; Opᵣ)
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Associative : Opₗ A B → Opᵣ A′ B → Set _
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Associative _∙ₗ_ _∙ᵣ_ = ∀ x m y → ((x ∙ₗ m) ∙ᵣ y) ≈ (x ∙ₗ (m ∙ᵣ y))
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{-# OPTIONS --cubical-compatible --safe #-}
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- open import Relation.Binary
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+ open import Relation.Binary using (Rel)
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module Algebra.Module.Definitions.Bi.Simultaneous
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{a b ℓb} (A : Set a) {B : Set b} (_≈_ : Rel B ℓb)
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where
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- open import Algebra.Module.Core
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+ open import Algebra.Module.Core using (Opₗ; Opᵣ)
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Coincident : Opₗ A B → Opᵣ A B → Set _
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Coincident _∙ₗ_ _∙ᵣ_ = ∀ x m → (x ∙ₗ m) ≈ (m ∙ᵣ x)
Original file line number Diff line number Diff line change @@ -19,8 +19,8 @@ module Algebra.Module.Definitions.Left
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------------------------------------------------------------------------
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-- Binary operations
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- open import Algebra.Core
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- open import Algebra.Module.Core
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+ open import Algebra.Core using (Op₂)
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+ open import Algebra.Module.Core using (Opₗ)
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------------------------------------------------------------------------
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-- Properties of operations
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------------------------------------------------------------------------
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-- Binary operations
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- open import Algebra.Core
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- open import Algebra.Module.Core
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+ open import Algebra.Core using (Op₂)
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+ open import Algebra.Module.Core using (Opᵣ)
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------------------------------------------------------------------------
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-- Properties of operations
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module Algebra.Module.Morphism.Construct.Composition where
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open import Algebra.Module.Bundles.Raw
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+ using (RawLeftSemimodule; RawLeftModule; RawRightSemimodule; RawRightModule;
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+ RawBisemimodule; RawBimodule; RawSemimodule; RawModule)
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open import Algebra.Module.Morphism.Structures
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- open import Algebra.Morphism.Construct.Composition
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+ open import Algebra.Morphism.Construct.Composition using (isMonoidHomomorphism; isGroupHomomorphism)
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open import Function.Base using (_∘_)
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- import Function.Construct.Composition as Func
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+ import Function.Construct.Composition as Func using (surjective)
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open import Level using (Level)
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open import Relation.Binary.Definitions using (Transitive)
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Original file line number Diff line number Diff line change @@ -19,7 +19,7 @@ open import Algebra.Module.Morphism.Structures
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; module SemimoduleMorphisms
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; module ModuleMorphisms
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)
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- open import Algebra.Morphism.Construct.Identity
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+ open import Algebra.Morphism.Construct.Identity using ( isMonoidHomomorphism; isGroupHomomorphism)
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open import Data.Product.Base using (_,_)
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open import Function.Base using (id)
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import Function.Construct.Identity as Id
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