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Diffstat (limited to 'examples/category-theory/Equalizer.gf')
| -rw-r--r-- | examples/category-theory/Equalizer.gf | 49 |
1 files changed, 0 insertions, 49 deletions
diff --git a/examples/category-theory/Equalizer.gf b/examples/category-theory/Equalizer.gf deleted file mode 100644 index 4e12bd199..000000000 --- a/examples/category-theory/Equalizer.gf +++ /dev/null @@ -1,49 +0,0 @@ -abstract Equalizer = Morphisms ** { - -cat Equalizer ({c} : Category) ({x,y,z} : Obj c) (f,g : Arrow x y) (e : Arrow z x) ; - -data equalizer : ({c} : Category) - -> ({x,y,z} : Obj c) - -> (f,g : Arrow x y) - -> (e : Arrow z x) - -> EqAr (comp f e) (comp g e) - -> Equalizer f g e ; - -fun idEqualizer : ({c} : Category) - -> ({x,y} : Obj c) - -> (f : Arrow x y) - -> Equalizer f f (id x) ; -def idEqualizer {c} {x} {y} f = equalizer f f (id x) (eqCompL f (eqRefl (id x))) ; - -fun equalizer2mono : ({c} : Category) - -> ({x,y,z} : Obj c) - -> (f,g : Arrow x y) - -> (e : Arrow z x) - -> Equalizer f g e - -> Mono e ; --- def equalizer2mono = ... - -cat CoEqualizer ({c} : Category) ({x,y,z} : Obj c) (e : Arrow y z) (f,g : Arrow x y) ; - -data coequalizer : ({c} : Category) - -> ({x,y,z} : Obj c) - -> (e : Arrow y z) - -> (f,g : Arrow x y) - -> EqAr (comp e f) (comp e g) - -> CoEqualizer e f g ; - -fun idCoEqualizer : ({c} : Category) - -> ({x,y} : Obj c) - -> (f : Arrow x y) - -> CoEqualizer (id y) f f ; -def idCoEqualizer {c} {x} {y} f = coequalizer (id y) f f (eqCompR (eqRefl (id y)) f) ; - -fun coequalizer2epi : ({c} : Category) - -> ({x,y,z} : Obj c) - -> ({e} : Arrow y z) - -> ({f,g} : Arrow x y) - -> CoEqualizer e f g - -> Epi e ; --- def coequalizer2epi = ... - -} |