| Copyright | (c) Erich Gut |
|---|---|
| License | BSD3 |
| Maintainer | zerich.gut@gmail.com |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
OAlg.Limes.EqualizersAndCoequalizers
Synopsis
- type Equalizers n = Limits Mlt Projective (Parallel LeftToRight) N2 n
- type Equalizer n = Limes Mlt Projective (Parallel LeftToRight) N2 n
- type EqualizerCone n = Cone Mlt Projective (Parallel LeftToRight) N2 n
- type EqualizerDiagram n = Diagram (Parallel LeftToRight) N2 n
- equalizers :: Multiplicative a => Products N2 a -> Equalizers N2 a -> Equalizers n a
- equalizers0 :: Multiplicative a => Products N2 a -> Equalizers N0 a
- equalizers1 :: Multiplicative a => Equalizers N1 a
- equalizers2 :: Multiplicative a => Equalizers N2 a -> Equalizers (n + 2) a
- equalizersOrnt :: Entity p => p -> Equalizers n (Orientation p)
- type Coequalizers n = Limits Mlt Injective (Parallel RightToLeft) N2 n
- type Coequalizer n = Limes Mlt Injective (Parallel RightToLeft) N2 n
- type CoequalizerCone n = Cone Mlt Injective (Parallel RightToLeft) N2 n
- type CoequalizerDiagram n = Diagram (Parallel RightToLeft) N2 n
- coequalizers :: Multiplicative a => Sums N2 a -> Coequalizers N2 a -> Coequalizers n a
- coequalizers' :: Multiplicative a => p n -> Sums N2 a -> Coequalizers N2 a -> Coequalizers n a
- coequalizersOrnt :: Entity p => p -> Coequalizers n (Orientation p)
- coeqlLimitsDuality :: Multiplicative a => LimitsDuality Mlt (Coequalizers n) (Equalizers n) a
Equalizers
type Equalizers n = Limits Mlt Projective (Parallel LeftToRight) N2 n Source #
equalizers for a Multiplicative structures.
type Equalizer n = Limes Mlt Projective (Parallel LeftToRight) N2 n Source #
equalizer as Limes.
type EqualizerCone n = Cone Mlt Projective (Parallel LeftToRight) N2 n Source #
Cone for a equalizer.
type EqualizerDiagram n = Diagram (Parallel LeftToRight) N2 n Source #
Diagram for a equalizer.
Construction
equalizers :: Multiplicative a => Products N2 a -> Equalizers N2 a -> Equalizers n a Source #
equalizers of n arrows given by products of two points and equalizers of two arrows.
equalizers0 :: Multiplicative a => Products N2 a -> Equalizers N0 a Source #
the induced equalizers of zero parallel arrows.
equalizers1 :: Multiplicative a => Equalizers N1 a Source #
equalizers of one parallel arrow, i.e. Minima.
equalizers2 :: Multiplicative a => Equalizers N2 a -> Equalizers (n + 2) a Source #
promoting equalizers.
Orientation
equalizersOrnt :: Entity p => p -> Equalizers n (Orientation p) Source #
equalizers for Orientation
Coequalizers
type Coequalizers n = Limits Mlt Injective (Parallel RightToLeft) N2 n Source #
coequalizers for a Multiplicative structure.
type Coequalizer n = Limes Mlt Injective (Parallel RightToLeft) N2 n Source #
coequalizer as 'Limes.
type CoequalizerCone n = Cone Mlt Injective (Parallel RightToLeft) N2 n Source #
Cone for a coequalizer.
type CoequalizerDiagram n = Diagram (Parallel RightToLeft) N2 n Source #
Diagram for a coequalizer.
Construction
coequalizers :: Multiplicative a => Sums N2 a -> Coequalizers N2 a -> Coequalizers n a Source #
coequalizers of n arrows given by sums of two points and coequalizers of two arrows.
coequalizers' :: Multiplicative a => p n -> Sums N2 a -> Coequalizers N2 a -> Coequalizers n a Source #
coequalizers given by a proxy for n.
Orientation
coequalizersOrnt :: Entity p => p -> Coequalizers n (Orientation p) Source #
coequalizers for Orientation.
Duality
coeqlLimitsDuality :: Multiplicative a => LimitsDuality Mlt (Coequalizers n) (Equalizers n) a Source #
duality between coequalizers and equalizers.