| Copyright | (c) Erich Gut |
|---|---|
| License | BSD3 |
| Maintainer | zerich.gut@gmail.com |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
OAlg.Limes.ProductsAndSums
Synopsis
- type Products n = Limits Mlt Projective Discrete n N0
- type Product n = Limes Mlt Projective Discrete n N0
- type ProductCone n = Cone Mlt Projective Discrete n N0
- type ProductDiagram n = Diagram Discrete n N0
- prdDiagram :: Oriented a => Diagram (Star From) (n + 1) n a -> ProductDiagram n a
- prdCone :: Multiplicative a => Diagram (Star From) (n + 1) n a -> ProductCone n a
- products :: Multiplicative a => Products N0 a -> Products N2 a -> Products n a
- products0 :: Multiplicative a => TerminalPoint a -> Products N0 a
- products1 :: Multiplicative a => Products N1 a
- products2 :: Multiplicative a => Products N2 a -> Products (n + 2) a
- prdConeOrnt :: Entity p => p -> FinList n p -> ProductCone n (Orientation p)
- productOrnt :: Entity p => p -> FinList n p -> Product n (Orientation p)
- productsOrnt :: Entity p => p -> Products n (Orientation p)
- type Sums n = Limits Mlt Injective Discrete n N0
- type Sum n = Limes Mlt Injective Discrete n N0
- type SumCone n = Cone Mlt Injective Discrete n N0
- type SumDiagram n = Diagram Discrete n N0
- sumLimitsDuality :: Multiplicative a => LimitsDuality Mlt (Sums n) (Products n) a
- sumDiagram :: Oriented a => Diagram (Star To) (n + 1) n a -> SumDiagram n a
- sumCone :: Multiplicative a => Diagram (Star To) (n + 1) n a -> SumCone n a
- sums :: Multiplicative a => Sums N0 a -> Sums N2 a -> Sums n a
- sums' :: Multiplicative a => p n -> Sums N0 a -> Sums N2 a -> Sums n a
- sums0 :: Multiplicative a => InitialPoint a -> Sums N0 a
- sums1 :: Multiplicative a => Sums N1 a
- sums2 :: Multiplicative a => Sums N2 a -> Sums (n + 2) a
- sumConeOrnt :: Entity p => p -> FinList n p -> SumCone n (Orientation p)
- sumOrnt :: Entity p => p -> FinList n p -> Sum n (Orientation p)
- sumsOrnt :: Entity p => p -> Sums n (Orientation p)
Products
type Products n = Limits Mlt Projective Discrete n N0 Source #
products for a Multiplicative structure.
type ProductCone n = Cone Mlt Projective Discrete n N0 Source #
Cone for a product.
Construction
prdDiagram :: Oriented a => Diagram (Star From) (n + 1) n a -> ProductDiagram n a Source #
the underlying product diagram.
prdCone :: Multiplicative a => Diagram (Star From) (n + 1) n a -> ProductCone n a Source #
the product cone.
products :: Multiplicative a => Products N0 a -> Products N2 a -> Products n a Source #
products of n points given by products of zero and two points.
products0 :: Multiplicative a => TerminalPoint a -> Products N0 a Source #
products of zero points given by a terminal point.
products2 :: Multiplicative a => Products N2 a -> Products (n + 2) a Source #
products of at least two points given by products of two points.
Orientation
prdConeOrnt :: Entity p => p -> FinList n p -> ProductCone n (Orientation p) Source #
product cone for Orientation.
productOrnt :: Entity p => p -> FinList n p -> Product n (Orientation p) Source #
product for Orientation.
productsOrnt :: Entity p => p -> Products n (Orientation p) Source #
products for Orientation.
Sums
Duality
sumLimitsDuality :: Multiplicative a => LimitsDuality Mlt (Sums n) (Products n) a Source #
duality between sums and products.
Construction
sumDiagram :: Oriented a => Diagram (Star To) (n + 1) n a -> SumDiagram n a Source #
the underlying sum diagram given by a sink diagram.
sumCone :: Multiplicative a => Diagram (Star To) (n + 1) n a -> SumCone n a Source #
the sum cone given by a sink diagram.
sums :: Multiplicative a => Sums N0 a -> Sums N2 a -> Sums n a Source #
sums of n points given by sums of zero and two points.
sums' :: Multiplicative a => p n -> Sums N0 a -> Sums N2 a -> Sums n a Source #
sums given by a proxy type for n.
sums0 :: Multiplicative a => InitialPoint a -> Sums N0 a Source #
sums of zero points given by a initial point.
sums2 :: Multiplicative a => Sums N2 a -> Sums (n + 2) a Source #
sums of at least two points given by sums of two points.
Orientation
sumConeOrnt :: Entity p => p -> FinList n p -> SumCone n (Orientation p) Source #
sum cone for Orientation.
sumOrnt :: Entity p => p -> FinList n p -> Sum n (Orientation p) Source #
sum for Orientation.
sumsOrnt :: Entity p => p -> Sums n (Orientation p) Source #
sums for Orientation.