net.categoricaldata.category

LocallyFinitelyGeneratedCategory

trait LocallyFinitelyGeneratedCategory extends SmallCategory

A LocallyFinitelyGeneratedCategory may have infinitely many objects, but each object sits at some integer level, and there are only finitely many objects at each level. Otherwise, the levels are completely ignored; in particular, they do not provide a grading or even a filtration.

Each pair of objects has a finite set of 'generators'. This means that every morphism between two objects can be written as some composition of 'generators' between some chain of objects (with no restrictions on the levels).

Self Type
LocallyFinitelyGeneratedCategory
Source
LocallyFinitelyGeneratedCategory.scala
Linear Supertypes
SmallCategory, Category, AnyRef, Any
Known Subclasses
Ordering
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Inherited
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  1. LocallyFinitelyGeneratedCategory
  2. SmallCategory
  3. Category
  4. AnyRef
  5. 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. abstract class FullSubcategory extends Wrapper with FinitelyGeneratedCategory

    Attributes
    protected
  6. class FullSubcategoryInclusion extends withLocallyFinitelyGeneratedTarget

    Attributes
    protected
  7. trait FunctorFrom extends Functor

    Attributes
    protected
  8. trait FunctorOver extends AnyRef

    Attributes
    protected
  9. trait FunctorTo extends Functor

    Attributes
    protected
  10. trait FunctorToSet extends FunctorToSet with withLocallyFinitelyGeneratedSource

  11. trait FunctorsToSet extends FunctorsToSet

  12. abstract type G

  13. trait Identity extends EndoFunctor

  14. type M = PathEquivalenceClass

  15. trait NaturalTransformationFrom extends NaturalTransformation

    Attributes
    protected
  16. trait NaturalTransformationOver extends NaturalTransformation

    Attributes
    protected
  17. trait NaturalTransformationTo extends NaturalTransformation

    Attributes
    protected
  18. trait NaturalTransformationToSet extends NaturalTransformationFrom with NaturalTransformationToSet

  19. abstract type O

    Definition Classes
    Category
  20. trait Opposite extends Category

    Attributes
    protected
  21. trait OppositeLocallyFinitelyGeneratedCategory extends LocallyFinitelyGeneratedCategory with ReversedGenerators

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

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

  24. trait ReversedGenerators extends SameObjects

  25. class RichPath extends AnyRef

    Attributes
    protected
  26. trait SameObjects extends AnyRef

  27. trait Wrapper extends LocallyFinitelyGeneratedCategory

    Attributes
    protected

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

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

  7. abstract val minimumLevel: Int

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

  9. abstract val opposite: LocallyFinitelyGeneratedCategory with ReversedGenerators

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

  11. 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.

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. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  8. def categoriesOver: CategoriesOver

    Definition Classes
    SmallCategory
  9. def clone(): AnyRef

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

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

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

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

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

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

    Definition Classes
    Category
  16. def finalize(): Unit

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  17. def fullSubcategory(spannedBy: List[O]): FinitelyGeneratedCategory

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

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

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

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

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

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

  24. val identityFunctor: Identity

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

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

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

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

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

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

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

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

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

    Definition Classes
    AnyRef
  34. def objectSet: FSet

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

    Attributes
    protected
  36. implicit def pathAsMorphism(p: Path): PathEquivalenceClass

  37. def source(m: M): O

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

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

  40. def toString(): String

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

  42. def truncationFunctorAtLevel(maximumLevel: Int): withLocallyFinitelyGeneratedTarget

  43. final def wait(): Unit

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

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

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

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

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

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

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

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

  52. object yoneda extends withLocallyFinitelyGeneratedSource

Inherited from SmallCategory

Inherited from Category

Inherited from AnyRef

Inherited from Any