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Diffstat (limited to 'src/Helium/Algebra/Morphism')
-rw-r--r-- | src/Helium/Algebra/Morphism/Structures.agda | 42 |
1 files changed, 42 insertions, 0 deletions
diff --git a/src/Helium/Algebra/Morphism/Structures.agda b/src/Helium/Algebra/Morphism/Structures.agda new file mode 100644 index 0000000..bf219ef --- /dev/null +++ b/src/Helium/Algebra/Morphism/Structures.agda @@ -0,0 +1,42 @@ +------------------------------------------------------------------------ +-- 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 |