net.categoricaldata.category

FinitelyPresentedCategory

trait FinitelyPresentedCategory extends FinitelyGeneratedCategory

Self Type
FinitelyPresentedCategory
Source
FinitelyPresentedCategory.scala
Linear Supertypes
Known Subclasses
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Inherited
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  1. FinitelyPresentedCategory
  2. FinitelyGeneratedCategory
  3. LocallyFinitelyGeneratedCategory
  4. SmallCategory
  5. Category
  6. AnyRef
  7. Any
Visibility
  1. Public
  2. All

Type Members

  1. trait CategoriesOver extends Category

    Attributes
    protected
  2. trait CategoryOver extends withSmallTarget

    Attributes
    protected
  3. abstract type D <: FunctorsToSet

  4. trait EndoFunctor extends FunctorFrom with FunctorTo with ParametrizedFunctor[Category.this.type, Category.this.type]

    Attributes
    protected
  5. trait FinitelyGeneratedCategoriesOver extends Category

  6. trait FinitelyGeneratedCategoryOver extends CategoryOver with withFinitelyGeneratedTarget

  7. trait FinitelyGeneratedFunctorOver extends FunctorOver

  8. abstract class FullSubcategory extends FullSubcategory with FinitelyPresentedCategory

    Attributes
    protected
    Definition Classes
    FinitelyPresentedCategoryLocallyFinitelyGeneratedCategory
  9. class FullSubcategoryInclusion extends FullSubcategoryInclusion with withFinitelyPresentedTarget

    Attributes
    protected
    Definition Classes
    FinitelyPresentedCategoryLocallyFinitelyGeneratedCategory
  10. trait FunctorFrom extends Functor

    Attributes
    protected
  11. trait FunctorOver extends AnyRef

    Attributes
    protected
  12. trait FunctorTo extends Functor

    Attributes
    protected
  13. trait FunctorToSet extends FunctorToSet with withFinitelyPresentedSource

  14. trait FunctorsToSet extends FunctorsToSet

  15. abstract type G

  16. trait Identity extends Identity with withFinitelyPresentedTarget

  17. type M = PathEquivalenceClass

  18. trait NaturalTransformationFrom extends NaturalTransformation

    Attributes
    protected
  19. trait NaturalTransformationOver extends NaturalTransformation

    Attributes
    protected
  20. trait NaturalTransformationTo extends NaturalTransformation

    Attributes
    protected
  21. trait NaturalTransformationToSet extends NaturalTransformationToSet

  22. abstract type O

    Definition Classes
    Category
  23. trait Opposite extends Category

    Attributes
    protected
  24. trait OppositeFinitelyGeneratedCategory extends FinitelyGeneratedCategory with OppositeLocallyFinitelyGeneratedCategory

    Attributes
    protected
  25. trait OppositeFinitelyPresentedCategory extends FinitelyPresentedCategory with OppositeFinitelyGeneratedCategory

  26. trait OppositeLocallyFinitelyGeneratedCategory extends LocallyFinitelyGeneratedCategory with ReversedGenerators

    Attributes
    protected
  27. type Path = Path[O, G]

  28. case class PathEquivalenceClass(representative: Path) extends Product with Serializable

  29. trait ReversedGenerators extends SameObjects

  30. class RichPath extends AnyRef

    Attributes
    protected
  31. trait SameObjects extends AnyRef

  32. trait Wrapper extends Wrapper with FinitelyPresentedCategory

Abstract Value Members

  1. abstract val functorsToSet: D

    Definition Classes
    SmallCategory
  2. abstract def generatorSource(g: G): O

  3. abstract def generatorTarget(g: G): O

  4. abstract def generators(source: O, target: O): List[G]

  5. abstract val maximumLevel: Int

    Definition Classes
    FinitelyGeneratedCategory
  6. abstract val minimumLevel: Int

  7. abstract def objectsAtLevel(k: Int): List[O]

  8. abstract def pathEquality(path1: Path, path2: Path): Boolean

  9. abstract def pathHashCode(path: Path): Int

    The only constraint on pathHashCode is the equal paths must give the same result.

    The only constraint on pathHashCode is the equal paths must give the same result. The extent possible, unequal paths should give different results, as long as this is a cheap calculation. Categories with normal forms override this automatically.

    Definition Classes
    LocallyFinitelyGeneratedCategory
  10. abstract def relations(source: O, target: O): List[(Path, Path)]

Concrete Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any
  3. final def ##(): Int

    Definition Classes
    AnyRef → Any
  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any
  6. object AllFunctorsToSet extends FunctorsToSet

  7. def allGenerators: List[G]

    Definition Classes
    FinitelyGeneratedCategory
  8. def allNontrivialWords: Iterable[Path]

    Definition Classes
    FinitelyGeneratedCategory
  9. def allRelations: List[(Path, Path)]

  10. def allWords: Iterable[Path]

    Definition Classes
    FinitelyGeneratedCategory
  11. def allWordsOfLength(k: Int): List[Path]

    Definition Classes
    FinitelyGeneratedCategory
  12. def allWordsUpToLength(k: Int): List[Path]

    Definition Classes
    FinitelyGeneratedCategory
  13. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  14. def categoriesOver: CategoriesOver

    Definition Classes
    SmallCategory
  15. def clone(): AnyRef

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  16. def compose(m1: M, m2: M): PathEquivalenceClass

  17. def compose(o: O, ms: List[M]): M

    Definition Classes
    Category
  18. def compose(m0: M, ms: M*): M

    Definition Classes
    Category
  19. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  20. def equals(other: Any): Boolean

    Definition Classes
    FinitelyPresentedCategory → AnyRef → Any
  21. def exponentiate(m: M, k: Int): M

    Definition Classes
    Category
  22. def finalize(): Unit

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  23. def findEquivalencesTo(other: FinitelyPresentedCategory): Iterable[Equivalence]

  24. def findIsomorphismsTo(other: FinitelyPresentedCategory): Iterable[Functor]

  25. def finitelyGeneratedCategoriesOver: FinitelyGeneratedCategoriesOver

    Definition Classes
    FinitelyGeneratedCategory
  26. def fullSubcategory(spannedBy: List[O]): FullSubcategory

  27. def fullSubcategoryInclusion(spannedBy: List[O]): FullSubcategoryInclusion

  28. implicit def generatorAsMorphism(g: G): M

  29. implicit def generatorAsPath(g: G): Path[O, G]

  30. def generatorsFrom(source: O): List[G]

  31. def generatorsTo(target: O): List[G]

  32. final def getClass(): java.lang.Class[_]

    Definition Classes
    AnyRef → Any
  33. def hashCode(): Int

    Definition Classes
    FinitelyPresentedCategory → AnyRef → Any
  34. def identity(o: O): PathEquivalenceClass

  35. val identityFunctor: Identity

    Definition Classes
    FinitelyPresentedCategoryCategory
  36. def internalize(t: NaturalTransformationToSet): M

    Definition Classes
    SmallCategory
  37. def internalize(f: FunctorToSet): O

    Definition Classes
    SmallCategory
  38. def isEquivalentTo(other: FinitelyPresentedCategory): Boolean

  39. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  40. def isIsomorphicTo(other: FinitelyPresentedCategory): Boolean

  41. def morphisms(source: O, target: O): Iterable[M]

  42. def morphismsOfLength(k: Int)(source: O, target: O): Set[M]

  43. def morphismsUpToLength(k: Int)(source: O, target: O): Set[M]

  44. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  45. final def notify(): Unit

    Definition Classes
    AnyRef
  46. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  47. def objectSet: FSet

  48. lazy val objects: List[O]

    Definition Classes
    FinitelyGeneratedCategory
  49. lazy val opposite: FinitelyGeneratedCategory with SameObjects with ReversedGenerators

  50. implicit def path2RichPath(path: Path): RichPath

    Attributes
    protected
    Definition Classes
    LocallyFinitelyGeneratedCategory
  51. implicit def pathAsMorphism(p: Path): PathEquivalenceClass

  52. def relationsFrom(source: O): List[(Path, Path)]

  53. def relationsTo(target: O): List[(Path, Path)]

  54. def source(m: M): O

  55. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  56. def target(m: M): O

  57. def toString(): String

    Definition Classes
    AnyRef → Any
  58. def truncateAtLevel(maximumLevel: Int): FinitelyGeneratedCategory

  59. def truncationFunctorAtLevel(maximumLevel: Int): withLocallyFinitelyGeneratedTarget

  60. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()
  61. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()
  62. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()
  63. def words(source: O, target: O): Iterable[Path]

  64. def wordsFrom(source: O): Iterable[Path]

  65. def wordsOfLength(k: Int)(source: O, target: O): List[Path]

  66. def wordsOfLengthFrom(k: Int)(source: O): List[Path]

  67. def wordsUpToLength(k: Int)(source: O, target: O): List[Path]

  68. def wordsUpToLengthFrom(k: Int)(source: O): List[Path]

  69. object yoneda extends withLocallyFinitelyGeneratedSource

Inherited from FinitelyGeneratedCategory

Inherited from SmallCategory

Inherited from Category

Inherited from AnyRef

Inherited from Any