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9032676 1 year ago
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23 changed files with 45 additions and 19 deletions
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      .gitignore
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      Groups/Core.agda
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      category-research.agda-lib
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      src/CategoricalRelation/Heterogeneous.agda
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      src/Categories/2-Category.agda
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      src/Functors/Bifunctor.agda
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      src/Functors/Core.agda
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      src/Groups/Core.agda
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      src/Limits/Core.agda
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      src/Morphisms/Isomorphism.agda
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.gitignore View File

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\#*.agda#
.#*.agda
.DS_Store
_build

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Groups/Core.agda View File

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module Groups.Core where
open import Relation.Binary.PropositionalEquality
open import Level
private
variable
ℓ : Level
record Group (G : Set ℓ) (𝑒 : G) (_∙_ : G → G → G) : Set ℓ where
field
assoc : ∀ {f g h} → (f ∙ g) ∙ h ≡ f ∙ (g ∙ h)
id : ∀ {g} → g ∙ 𝑒 ≡ 𝑒 ∙ g
invₗ : ∀ {g h} → g ∙ h ≡ 𝑒
invᵣ : ∀ {g h} → 𝑒 ≡ h ∙ g

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category-research.agda-lib View File

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name: category-research
depend: standard-library
include: src

CategoricalRelation/Heterogeneous.agda → src/CategoricalRelation/Heterogeneous.agda View File

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open import Level
module CategoricalRelation.Heterogeneous where
open import Level
open import Categories.Core using (Category; Obj; _[_,_])
open import Relation.Binary.PropositionalEquality using (_≡_; refl; subst)

Categories/2-Category.agda → src/Categories/2-Category.agda View File


Categories/Comma.agda → src/Categories/Comma.agda View File


Categories/Core.agda → src/Categories/Core.agda View File


Categories/Product.agda → src/Categories/Product.agda View File


Categories/Sets.agda → src/Categories/Sets.agda View File


Functors/Adjunction.agda → src/Functors/Adjunction.agda View File


Functors/Bifunctor.agda → src/Functors/Bifunctor.agda View File


Functors/Core.agda → src/Functors/Core.agda View File


Functors/Homfunctor.agda → src/Functors/Homfunctor.agda View File


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src/Groups/Core.agda View File

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{-# OPTIONS --allow-unsolved-metas #-}
module Groups.Core where
open import Relation.Binary.PropositionalEquality using (refl; _≡_; sym; cong)
open import Level
private
variable
ℓ : Level
record Group (G : Set ℓ) : Set ℓ where
infixr 9 _∙_
field
𝑒 : G
_∙_ : G → G → G
_⁻¹ : G → G
field
assocₗ : ∀ 𝑥 𝑦 𝑧 → (𝑥 ∙ 𝑦) ∙ 𝑧 ≡ 𝑥 ∙ (𝑦 ∙ 𝑧)
assocᵣ : ∀ 𝑥 𝑦 𝑧 → 𝑥 ∙ (𝑦 ∙ 𝑧) ≡ (𝑥 ∙ 𝑦) ∙ 𝑧
idₗ : ∀ 𝑥 → 𝑥 ∙ 𝑒 ≡ 𝑥
idᵣ : ∀ 𝑥 → 𝑒 ∙ 𝑥 ≡ 𝑥
invₗ : ∀ 𝑥 → 𝑥 ∙ (𝑥 ⁻¹) ≡ 𝑒
invᵣ : ∀ 𝑥 → (𝑥 ⁻¹) ∙ 𝑥 ≡ 𝑒
record CommutativeGroup (G : Set ℓ) {𝐺 : Group G} : Set ℓ where
open Group 𝐺 using (_∙_)
field
comm : ∀ 𝑥 𝑦 → 𝑥 ∙ 𝑦 ≡ 𝑦 ∙ 𝑥
module GroupProp {G : Set ℓ} {𝐺 : Group G} where
open Group 𝐺
-- Cancellation
cancelₗ : (a g h : G) → g ∙ a ≡ h ∙ a → g ≡ h
cancelₗ a g h p = {!!}
cancelᵣ : (a g h : G) → a ∙ g ≡ a ∙ h → g ≡ h
cancelᵣ a g h p = {!!}

Limits/Core.agda → src/Limits/Core.agda View File


Monads/Core.agda → src/Monads/Core.agda View File


Morphisms/Homomorphism.agda → src/Morphisms/Homomorphism.agda View File


Morphisms/Isomorphism.agda → src/Morphisms/Isomorphism.agda View File


NaturalTransformations/Core.agda → src/NaturalTransformations/Core.agda View File


Objects/Coproduct.agda → src/Objects/Coproduct.agda View File


Objects/Product.agda → src/Objects/Product.agda View File


Yoneda/YonedaEmbedding.agda → src/Yoneda/YonedaEmbedding.agda View File


Yoneda/YonedaLemma.agda → src/Yoneda/YonedaLemma.agda View File


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