net.categoricaldata.category

FinitelyGeneratedCategory

trait FinitelyGeneratedCategory extends LocallyFinitelyGeneratedCategory

A FinitelyGeneratedCategory is just a LocallyFinitelyGeneratedCategory with finitely many levels (and so finitely many objects and generators).

Self Type
FinitelyGeneratedCategory
Source
FinitelyGeneratedCategory.scala
Linear Supertypes
Known Subclasses
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Inherited
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  1. FinitelyGeneratedCategory
  2. LocallyFinitelyGeneratedCategory
  3. SmallCategory
  4. Category
  5. AnyRef
  6. 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 Wrapper with FinitelyGeneratedCategory

    Attributes
    protected
  9. class FullSubcategoryInclusion extends withLocallyFinitelyGeneratedTarget

    Attributes
    protected
  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 withFinitelyGeneratedSource

  14. trait FunctorsToSet extends FunctorsToSet

  15. abstract type G

  16. trait Identity extends Identity with withFinitelyGeneratedTarget

    Definition Classes
    FinitelyGeneratedCategoryCategory
  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 OppositeLocallyFinitelyGeneratedCategory extends LocallyFinitelyGeneratedCategory with ReversedGenerators

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

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

  28. trait ReversedGenerators extends SameObjects

  29. class RichPath extends AnyRef

    Attributes
    protected
  30. trait SameObjects extends AnyRef

  31. trait Wrapper extends Wrapper with FinitelyGeneratedCategory

    Attributes
    protected
    Definition Classes
    FinitelyGeneratedCategoryLocallyFinitelyGeneratedCategory

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

  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

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]

  8. def allNontrivialWords: Iterable[Path]

  9. def allWords: Iterable[Path]

  10. def allWordsOfLength(k: Int): List[Path]

  11. def allWordsUpToLength(k: Int): List[Path]

  12. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  13. def categoriesOver: CategoriesOver

    Definition Classes
    SmallCategory
  14. def clone(): AnyRef

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

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

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

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

    Definition Classes
    AnyRef
  19. def equals(arg0: Any): Boolean

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

    Definition Classes
    Category
  21. def finalize(): Unit

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  22. def finitelyGeneratedCategoriesOver: FinitelyGeneratedCategoriesOver

  23. def fullSubcategory(spannedBy: List[O]): FinitelyGeneratedCategory

  24. def fullSubcategoryInclusion(spannedBy: List[O]): withLocallyFinitelyGeneratedTarget

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

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

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

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

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

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

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

  32. val identityFunctor: Identity

    Definition Classes
    Category
  33. def internalize(t: NaturalTransformationToSet): M

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

    Definition Classes
    SmallCategory
  35. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  36. def morphisms(source: O, target: O): Iterable[M]

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

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

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

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

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

    Definition Classes
    AnyRef
  42. def objectSet: FSet

  43. lazy val objects: List[O]

  44. lazy val opposite: FinitelyGeneratedCategory with SameObjects with ReversedGenerators

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

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

  47. def source(m: M): O

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

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

  50. def toString(): String

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

  52. def truncationFunctorAtLevel(maximumLevel: Int): withLocallyFinitelyGeneratedTarget

  53. final def wait(): Unit

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

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

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

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

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

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

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

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

  62. object yoneda extends withLocallyFinitelyGeneratedSource

Inherited from SmallCategory

Inherited from Category

Inherited from AnyRef

Inherited from Any