diff options
| author | krasimir <krasimir@chalmers.se> | 2010-02-15 10:35:24 +0000 |
|---|---|---|
| committer | krasimir <krasimir@chalmers.se> | 2010-02-15 10:35:24 +0000 |
| commit | 61287f39259bdca55ba9874d369d2d2191bb1baf (patch) | |
| tree | 01bf7c8cc0febacb5cc107633efd6baaa535892a /examples/category-theory/InitialAndTerminal.gf | |
| parent | af48998ef6ca342573e2758be708f81793c47f27 (diff) | |
more category theory -> morphisms, initial and terminal objects
Diffstat (limited to 'examples/category-theory/InitialAndTerminal.gf')
| -rw-r--r-- | examples/category-theory/InitialAndTerminal.gf | 35 |
1 files changed, 35 insertions, 0 deletions
diff --git a/examples/category-theory/InitialAndTerminal.gf b/examples/category-theory/InitialAndTerminal.gf new file mode 100644 index 000000000..7ac7b0864 --- /dev/null +++ b/examples/category-theory/InitialAndTerminal.gf @@ -0,0 +1,35 @@ +abstract InitialAndTerminal = Morphisms ** {
+
+cat Initial (c : Category) ;
+data initial : ({c} : Category)
+ -> (x : El c)
+ -> ((y : El c) -> Arrow x y)
+ -> Initial c ;
+
+fun initEl : ({c} : Category)
+ -> Initial c
+ -> El c ;
+def initEl (initial x f) = x ;
+
+fun initials2iso : ({c} : Category)
+ -> ({x,y} : Initial c)
+ -> Iso (initEl x) (initEl y) ;
+-- def initials2iso = .. ;
+
+cat Terminal (c : Category) ;
+data terminal : ({c} : Category)
+ -> (y : El c)
+ -> ((x : El c) -> Arrow x y)
+ -> Terminal c ;
+
+fun termEl : ({c} : Category)
+ -> Terminal c
+ -> El c ;
+def termEl (terminal x f) = x ;
+
+fun terminals2iso : ({c} : Category)
+ -> ({x,y} : Terminal c)
+ -> Iso (termEl x) (termEl y) ;
+-- def terminals2iso = .. ;
+
+}
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