Modified verion of 9.1.9
This commit is contained in:
parent
7eac677efb
commit
7fcd8e631a
|
@ -337,6 +337,8 @@ module _ {ℓa ℓb : Level} (ℂ : RawCategory ℓa ℓb) where
|
|||
private
|
||||
q* : Arrow b b'
|
||||
q* = fst (idToIso b b' q)
|
||||
p* : Arrow a a'
|
||||
p* = fst (idToIso _ _ p)
|
||||
p~ : Arrow a' a
|
||||
p~ = fst (snd (idToIso _ _ p))
|
||||
pq : Arrow a b ≡ Arrow a' b'
|
||||
|
@ -365,6 +367,17 @@ module _ {ℓa ℓb : Level} (ℂ : RawCategory ℓa ℓb) where
|
|||
9-1-9 : coe pq f ≡ q* <<< f <<< p~
|
||||
9-1-9 = pathJ D d a' p
|
||||
|
||||
9-1-9' : coe pq f <<< p* ≡ q* <<< f
|
||||
9-1-9' = begin
|
||||
coe pq f <<< p* ≡⟨ cong (_<<< p*) 9-1-9 ⟩
|
||||
q* <<< f <<< p~ <<< p* ≡⟨ sym isAssociative ⟩
|
||||
q* <<< f <<< (p~ <<< p*) ≡⟨ cong (λ φ → q* <<< f <<< φ) lem ⟩
|
||||
q* <<< f <<< identity ≡⟨ rightIdentity ⟩
|
||||
q* <<< f ∎
|
||||
where
|
||||
lem : p~ <<< p* ≡ identity
|
||||
lem = fst (snd (snd (idToIso _ _ p)))
|
||||
|
||||
-- | All projections are propositions.
|
||||
module Propositionality where
|
||||
-- | Terminal objects are propositional - a.k.a uniqueness of terminal
|
||||
|
|
|
@ -250,11 +250,10 @@ module Try0 {ℓa ℓb : Level} {ℂ : Category ℓa ℓb}
|
|||
≈ ((X , xa , xb) ≅ (Y , ya , yb))
|
||||
step2
|
||||
= ( λ{ ((f , f~ , inv-f) , p , q)
|
||||
→ ( f , (let r = fromPathP p in {!r!}) , {!!})
|
||||
, ( (f~ , {!!} , {!!})
|
||||
, lemA (fst inv-f)
|
||||
, lemA (snd inv-f)
|
||||
)
|
||||
→ ( f , {!ℂ.9-1-9'!} , {!!})
|
||||
, ( f~ , {!!} , {!!})
|
||||
, lemA (fst inv-f)
|
||||
, lemA (snd inv-f)
|
||||
}
|
||||
)
|
||||
, (λ{ (f , f~ , inv-f , inv-f~) →
|
||||
|
|
Loading…
Reference in a new issue