Modified verion of 9.1.9

This commit is contained in:
Frederik Hanghøj Iversen 2018-04-12 11:21:05 +02:00
parent 7eac677efb
commit 7fcd8e631a
2 changed files with 17 additions and 5 deletions

View file

@ -337,6 +337,8 @@ module _ {a b : Level} ( : RawCategory a b) 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 _ {a b : Level} ( : RawCategory a b) 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

View file

@ -250,11 +250,10 @@ module Try0 {a b : Level} { : Category a b}
((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 , {!.9-1-9'!} , {!!})
, ( f~ , {!!} , {!!})
, lemA (fst inv-f)
, lemA (snd inv-f)
}
)
, (λ{ (f , f~ , inv-f , inv-f~)