Re-add eqpair
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@ -10,13 +10,15 @@ open import Data.Product renaming (proj₁ to fst ; proj₂ to snd)
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open import Cat.Category
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open import Cat.Functor
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-- Tip from Andrea:
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-- Use co-patterns - they help with showing more understandable types in goals.
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lift-eq : ∀ {ℓ} {A B : Set ℓ} {a a' : A} {b b' : B} → a ≡ a' → b ≡ b' → (a , b) ≡ (a' , b')
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fst (lift-eq a b i) = a i
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snd (lift-eq a b i) = b i
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--lift-eq a b = λ i → a i , b i
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eqpair : ∀ {ℓa ℓb} {A : Set ℓa} {B : Set ℓb} {a a' : A} {b b' : B}
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→ a ≡ a' → b ≡ b' → (a , b) ≡ (a' , b')
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eqpair eqa eqb i = eqa i , eqb i
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open Functor
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open Category
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@ -11,12 +11,10 @@ module _ {ℓ ℓ' : Level} (ℂ : Category ℓ ℓ') where
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open module ℂ = Category ℂ
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Obj = ℂ.Object
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Path : ( a b : Obj ) → Set ℓ'
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Path a b = undefined
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postulate emptyPath : (o : Obj) → Path o o
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postulate concatenate : {a b c : Obj} → Path b c → Path a b → Path a c
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postulate
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Path : ( a b : Obj ) → Set ℓ'
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emptyPath : (o : Obj) → Path o o
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concatenate : {a b c : Obj} → Path b c → Path a b → Path a c
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private
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module _ {A B C D : Obj} {r : Path A B} {q : Path B C} {p : Path C D} where
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