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the oposites of two equal arrows are equal arrows

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krasimir
2010-02-22 14:38:13 +00:00
parent 59d640088e
commit bcf4bc7d23
1 changed files with 10 additions and 2 deletions
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8
examples/category-theory/Categories.gf
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@@ -78,6 +78,14 @@ abstract Categories = {
def id {Op c} (opEl {c} x) = opAr (id x) ; def id {Op c} (opEl {c} x) = opAr (id x) ;
def comp {Op c} {opEl {c} x} {opEl {c} y} {opEl {c} z} (opAr {c} {y} {z} f) (opAr {c} {z} {x} g) = opAr (comp g f) ; def comp {Op c} {opEl {c} x} {opEl {c} y} {opEl {c} z} (opAr {c} {y} {z} f) (opAr {c} {z} {x} g) = opAr (comp g f) ;
fun eqOp : ({c} : Category)
-> ({x,y} : El c)
-> ({f} : Arrow x y)
-> ({g} : Arrow x y)
-> EqAr f g
-> EqAr (opAr f) (opAr g) ;
def eqOp {c} {x} {y} {f} {f} (eqRefl {c} {x} {y} f) = eqRefl (opAr f) ;
data Slash : (c : Category) data Slash : (c : Category)
-> (x : El c) -> (x : El c)
-> Category ; -> Category ;