Mercurial > hg > Members > kono > Proof > category
diff pullback.agda @ 292:a84fab7cf46a
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Wed, 25 Sep 2013 18:15:43 +0900 |
parents | c8e26650ddf9 |
children | fb0ab8c72e15 |
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--- a/pullback.agda Wed Sep 25 18:07:58 2013 +0900 +++ b/pullback.agda Wed Sep 25 18:15:43 2013 +0900 @@ -473,18 +473,18 @@ { η : NTrans A A identityFunctor ( U ○ F ) } { ε : NTrans B B ( F ○ U ) identityFunctor } → ( adj : Adjunction A B U F η ε ) → Limit A I (U ○ Γ) (FObj U lim) (ta1 B Γ lim tb limit U ) -adjoint-preseve-limit B Γ lim tb limit {U} {F} {η} {ε} adj = record { +adjoint-preseve-limit B Γ lim tb limitb {U} {F} {η} {ε} adj = record { limit = λ a t → limit1 a t ; t0f=t = λ {a t i } → t0f=t1 {a} {t} {i} ; limit-uniqueness = λ {a} {t} {f} t=f → limit-uniqueness1 {a} {t} {f} t=f } where - ta = ta1 B Γ lim tb limit U + ta = ta1 B Γ lim tb limitb U limit1 : (a : Obj A) → NTrans I A (K A I a) (U ○ Γ) → Hom A a (FObj U lim) limit1 a t = let open ≈-Reasoning (A) in ? t0f=t1 : {a : Obj A} {t : NTrans I A (K A I a) (U ○ Γ)} {i : Obj I} → A [ A [ TMap ta i o limit1 a t ] ≈ TMap t i ] - t0f=t1 {a} {t} {i} = let open ≈-Reasoning (A) in ? + t0f=t1 {a} {t} {i} = let open ≈-Reasoning (A) in {!!} limit-uniqueness1 : {a : Obj A} {t : NTrans I A (K A I a) (U ○ Γ)} {f : Hom A a (FObj U lim)} → ({i : Obj I} → A [ A [ TMap ta i o f ] ≈ TMap t i ]) → A [ limit1 a t ≈ f ] - limit-uniqueness1 {a} {t} {f} lim=t = let open ≈-Reasoning (A) in ? + limit-uniqueness1 {a} {t} {f} lim=t = let open ≈-Reasoning (A) in {!!}