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-------------------------------------------------------------------------
--- Agda Helium
---
--- Redefine Ring monomorphisms to resolve problems with overloading.
-------------------------------------------------------------------------
-
-{-# OPTIONS --safe --without-K #-}
-
-module Helium.Algebra.Morphism.Structures where
-
-open import Algebra.Bundles using (RawRing)
-open import Algebra.Morphism.Structures
- hiding (IsRingHomomorphism; module RingMorphisms)
-open import Level using (Level; _⊔_)
-
-private
- variable
- a b ℓ₁ ℓ₂ : Level
-
-module RingMorphisms (R₁ : RawRing a ℓ₁) (R₂ : RawRing b ℓ₂) where
- module R₁ = RawRing R₁ renaming (Carrier to A)
- module R₂ = RawRing R₂ renaming (Carrier to B)
- open R₁ using (A)
- open R₂ using (B)
-
- private
- module +′ = GroupMorphisms R₁.+-rawGroup R₂.+-rawGroup
- module *′ = MonoidMorphisms R₁.*-rawMonoid R₂.*-rawMonoid
-
- record IsRingHomomorphism (⟦_⟧ : A → B) : Set (a ⊔ ℓ₁ ⊔ ℓ₂) where
- field
- +-isGroupHomomorphism : +′.IsGroupHomomorphism ⟦_⟧
- *-isMonoidHomomorphism : *′.IsMonoidHomomorphism ⟦_⟧
-
- open +′.IsGroupHomomorphism +-isGroupHomomorphism public
- renaming (homo to +-homo; ε-homo to 0#-homo; ⁻¹-homo to -‿homo)
-
- open *′.IsMonoidHomomorphism *-isMonoidHomomorphism public
- hiding (⟦⟧-cong)
- renaming (homo to *-homo; ε-homo to 1#-homo)
-
-open RingMorphisms public