Mercurial > hg > Members > kono > Proof > category
changeset 1006:444d2aba55eb
yoneda done
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
---|---|
date | Wed, 10 Mar 2021 09:22:12 +0900 |
parents | fd2d54dd2197 |
children | 62c8d989cacb |
files | src/yoneda.agda |
diffstat | 1 files changed, 0 insertions(+), 17 deletions(-) [+] |
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--- a/src/yoneda.agda Wed Mar 10 09:06:57 2021 +0900 +++ b/src/yoneda.agda Wed Mar 10 09:22:12 2021 +0900 @@ -345,23 +345,6 @@ open CatSurjective --- CatEpiR : {c : Level } (F : Functor (Sets {c}) (Sets {c})) --- → {a a' : Obj Sets } {b : Obj Sets} (g h : Hom Sets (FObj F a') b) --- → ( ( f : {a a' b : Obj Sets} (g : Hom Sets (FObj F a) b) → Hom Sets a a' ) --- → (Sets [ Sets [ g o FMap F (f g) ] ≈ Sets [ h o FMap F (f h) ] ] → Sets [ g ≈ h ]) ) --- → CatSurjective Sets Sets F --- CatEpiR F g h eq = record { sur = λ {a} {a'} g → sur0 {a} {a'} g ; surjective = ylem22 } where --- sur0 : {a a' : Obj Sets} (g : Hom Sets (FObj F a) (FObj F a')) → Hom Sets a a' --- sur0 {a} {a'} g = {!!} --- ylem22 : {a a' : Obj Sets} (g : Hom Sets (FObj F a) (FObj F a')) → Sets [ FMap F (sur0 g) ≈ g ] --- ylem22 g = begin --- FMap F (sur0 g) ≈⟨ {!!} ⟩ --- Sets [ FMap F {!!} o FMap F {!!} ] ≈⟨ {!!} ⟩ --- Sets [ g o Sets [ FMap F {!!} o FMap F {!!} ] ] ≈⟨ {!!} ⟩ --- g ∎ --- where --- open ≈-Reasoning Sets - CatEpi : {c : Level} (F : Functor (Sets {c}) (Sets {c})) → (s : CatSurjective Sets Sets F ) → {a a' : Obj Sets } {b : Obj Sets} (g h : Hom Sets (FObj F a') b)