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Tidy up groups (#64)

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Patrick Stevens
2019-11-03 17:12:48 +00:00
committed by GitHub
parent e4daab7153
commit d95f510cdd
42 changed files with 1438 additions and 1038 deletions
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Categories/Examples.agda Normal file
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{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Numbers.Naturals.Order
open import Vectors
open import Semirings.Definition
open import Categories.Definition
open import Groups.Definition
module Categories.Examples where
SET : {a : _} → Category {lsuc a} {a}
Category.objects (SET {a}) = Set a
Category.arrows (SET {a}) = λ a b → (a → b)
Category.id (SET {a}) = λ x → λ y → y
Category._∘_ (SET {a}) = λ f g → λ x → f (g x)
Category.rightId (SET {a}) = λ f → refl
Category.leftId (SET {a}) = λ f → refl
Category.compositionAssociative (SET {a}) = λ f g h → refl
GROUP : {a : _} → Category {lsuc a} {a}
Category.objects (GROUP {a}) = Group {! !} {! !}
Category.arrows (GROUP {a}) = {! !}
Category.id (GROUP {a}) = {! !}
Category._∘_ (GROUP {a}) = {! !}
Category.rightId (GROUP {a}) = {! !}
Category.leftId (GROUP {a}) = {! !}
Category.compositionAssociative (GROUP {a}) = {! !}