| Copyright | (c) Erich Gut |
|---|---|
| License | BSD3 |
| Maintainer | zerich.gut@gmail.com |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
OAlg.Limes.TerminalAndInitialPoint
Description
terminal and initial point within a Multiplicative structure, i.e. limits of
Diagram Empty
Synopsis
- type Terminals = Limits Mlt Projective 'Empty N0 N0
- type TerminalPoint = Limes Mlt Projective 'Empty N0 N0
- type TerminalCone = Cone Mlt Projective 'Empty N0 N0
- type TerminalDiagram = Diagram 'Empty N0 N0
- trmDiagram :: TerminalDiagram a
- trmCone :: Multiplicative a => Point a -> TerminalCone a
- terminalPointOrnt :: Entity p => p -> TerminalPoint (Orientation p)
- trmsOrnt :: Entity p => p -> Terminals (Orientation p)
- type Initials = Limits Mlt Injective 'Empty N0 N0
- type InitialPoint = Limes Mlt Injective 'Empty N0 N0
- type InitialCone = Cone Mlt Injective 'Empty N0 N0
- type InitialDiagram = Diagram 'Empty N0 N0
- intDiagram :: InitialDiagram a
- intCone :: Multiplicative a => Point a -> InitialCone a
- initialPointOrnt :: Entity p => p -> InitialPoint (Orientation p)
- intsOrnt :: Entity p => p -> Initials (Orientation p)
- trmDiagramDuality :: Oriented a => DiagramDuality TerminalDiagram InitialDiagram a
- trmConeDuality :: Multiplicative a => ConeDuality Mlt TerminalCone InitialCone a
- trmLimesDuality :: Multiplicative a => LimesDuality Mlt TerminalPoint InitialPoint a
- trmLimitsDuality :: Multiplicative a => LimitsDuality Mlt Terminals Initials a
- intDiagramDuality :: Oriented a => DiagramDuality InitialDiagram TerminalDiagram a
- intConeDuality :: Multiplicative a => ConeDuality Mlt InitialCone TerminalCone a
- intLimesDuality :: Multiplicative a => LimesDuality Mlt InitialPoint TerminalPoint a
- intLimitsDuality :: Multiplicative a => LimitsDuality Mlt Initials Terminals a
Terminal
type Terminals = Limits Mlt Projective 'Empty N0 N0 Source #
terminal point within a Multiplicative structure.
type TerminalPoint = Limes Mlt Projective 'Empty N0 N0 Source #
terminal point as Limes.
type TerminalCone = Cone Mlt Projective 'Empty N0 N0 Source #
Cone for a terminal point.
trmDiagram :: TerminalDiagram a Source #
the terminal diagram.
trmCone :: Multiplicative a => Point a -> TerminalCone a Source #
the terminal cone of a given point.
Orientation
terminalPointOrnt :: Entity p => p -> TerminalPoint (Orientation p) Source #
the terminal limes of a given point p.
trmsOrnt :: Entity p => p -> Terminals (Orientation p) Source #
terminals for Orientation.
Initial
type Initials = Limits Mlt Injective 'Empty N0 N0 Source #
initial point within a Multiplicative structure.
intDiagram :: InitialDiagram a Source #
the initial diagram.
intCone :: Multiplicative a => Point a -> InitialCone a Source #
the initial cone of a given point.
Orientation
initialPointOrnt :: Entity p => p -> InitialPoint (Orientation p) Source #
initial point for Orientation.
Duality
Terminal
trmDiagramDuality :: Oriented a => DiagramDuality TerminalDiagram InitialDiagram a Source #
terminal Diagram duality.
trmConeDuality :: Multiplicative a => ConeDuality Mlt TerminalCone InitialCone a Source #
terminal Cone duality.
trmLimesDuality :: Multiplicative a => LimesDuality Mlt TerminalPoint InitialPoint a Source #
terminal Limes duality.
trmLimitsDuality :: Multiplicative a => LimitsDuality Mlt Terminals Initials a Source #
terminal Limits duality.
Initial
intDiagramDuality :: Oriented a => DiagramDuality InitialDiagram TerminalDiagram a Source #
initial Diagram duality.
intConeDuality :: Multiplicative a => ConeDuality Mlt InitialCone TerminalCone a Source #
initial Cone duality.
intLimesDuality :: Multiplicative a => LimesDuality Mlt InitialPoint TerminalPoint a Source #
initial Limes duality.
intLimitsDuality :: Multiplicative a => LimitsDuality Mlt Initials Terminals a Source #
initial Limits duality.