Mercurial > hg > Members > kono > Proof > category
diff SetsCompleteness.agda @ 681:bd8f7346f252
fix Product and pullback
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Tue, 07 Nov 2017 17:12:08 +0900 |
parents | faf48511f69d |
children | 917e51be9bbf |
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--- a/SetsCompleteness.agda Mon Nov 06 10:10:55 2017 +0900 +++ b/SetsCompleteness.agda Tue Nov 07 17:12:08 2017 +0900 @@ -26,12 +26,12 @@ open Σ public -SetsProduct : { c₂ : Level} → Product ( Sets { c₂} ) -SetsProduct { c₂ } = record { - product = λ a b → Σ a b - ; π1 = λ a b → λ ab → (proj₁ ab) - ; π2 = λ a b → λ ab → (proj₂ ab) - ; isProduct = λ a b → record { +SetsProduct : { c₂ : Level} → ( a b : Obj (Sets {c₂})) → Product ( Sets { c₂} ) a b +SetsProduct { c₂ } a b = record { + product = Σ a b + ; π1 = λ ab → (proj₁ ab) + ; π2 = λ ab → (proj₂ ab) + ; isProduct = record { _×_ = λ f g x → record { proj₁ = f x ; proj₂ = g x } -- ( f x , g x ) ; π1fxg=f = refl ; π2fxg=g = refl