Struct FinCategory

pub struct FinCategory<V, E, S = RandomState> { /* private fields */ }

A finite category with explicitly defined composition law.

Such a category is not just finitely presented, but actually finite. The composition law is defined by a hash map on pairs of morphism generators. While very special, finite categories show up surprisingly often as schemas or theories. For example, the schemas for graphs, symmetric graphs, reflexive graphs, and symmetric reflexive graphs are all finite.

Implementations

impl<V, E, S> FinCategory<V, E, S>

where V: Eq + Hash + Clone, E: Eq + Hash + Clone, S: BuildHasher,

pub fn generators(&self) -> &(impl FinGraph<V = V, E = E> + use<V, E, S>)

Graph of generators of the finite category.

pub fn add_ob_generator(&mut self, v: V) -> bool

Adds an object generator, returning whether it is new.

pub fn add_ob_generators<T>(&mut self, iter: T)

where T: IntoIterator<Item = V>,

Adds multiple object generators.

pub fn add_mor_generator(&mut self, e: E, dom: V, cod: V) -> bool

Adds a morphism generator, returning whether it is new.

pub fn set_composite(&mut self, d: E, e: E, f: FinMor<V, E>)

Sets the value of a binary composite.

pub fn iter_invalid(&self) -> impl Iterator<Item = InvalidFinCategory<E>> + '_

Iterates over failures to be a well-defined finite category.

Trait Implementations

impl<V, E, S> Category for FinCategory<V, E, S>

where V: Eq + Hash + Clone, E: Eq + Hash + Clone, S: BuildHasher,

type Ob = V

Type of objects in category.

type Mor = FinMor<V, E>

Type of morphisms in category.

fn has_ob(&self, x: &V) -> bool

Does the category contain the value as an object?

fn has_mor(&self, f: &FinMor<V, E>) -> bool

Does the category contain the value as a morphism?

fn dom(&self, f: &FinMor<V, E>) -> V

Gets the domain of a morphism in the category.

fn cod(&self, f: &FinMor<V, E>) -> V

Gets the codomain of a morphism in the category.

fn compose(&self, path: Path<V, FinMor<V, E>>) -> FinMor<V, E>

Composes a path of morphisms in the category.

fn compose2(&self, f: FinMor<V, E>, g: FinMor<V, E>) -> FinMor<V, E>

Composes a pair of morphisms with compatible (co)domains.

fn id(&self, x: V) -> FinMor<V, E>

Constructs the identity morphism at an object.

impl<V: Clone, E: Clone, S: Clone> Clone for FinCategory<V, E, S>

fn clone(&self) -> FinCategory<V, E, S>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<V: Debug, E: Debug, S: Debug> Debug for FinCategory<V, E, S>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<V, E, S> Default for FinCategory<V, E, S>

where S: Default,

fn default() -> Self

Returns the “default value” for a type.

impl<V, E, S> FgCategory for FinCategory<V, E, S>

where V: Eq + Hash + Clone, E: Eq + Hash + Clone, S: BuildHasher,

type ObGen = V

Type of an object generator.

type MorGen = E

Type of a morphism generator

fn ob_generators(&self) -> impl Iterator<Item = Self::ObGen>

Iterates over object generators.

fn mor_generators(&self) -> impl Iterator<Item = Self::MorGen>

Iterates over morphism generators.

fn mor_generator_dom(&self, f: &Self::MorGen) -> Self::Ob

The domain of a morphism generator

fn mor_generator_cod(&self, f: &Self::MorGen) -> Self::Ob

The codomain of a morphism generator

fn objects(&self) -> impl Iterator<Item = Self::Ob>

Iterates over basic objects.

fn morphisms(&self) -> impl Iterator<Item = Self::Mor>

Iterates over basic morphisms.

impl<V, E, S> PartialEq for FinCategory<V, E, S>

where V: Eq + Hash, E: Eq + Hash, S: BuildHasher,

fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<V, E, S> Validate for FinCategory<V, E, S>

where V: Eq + Hash + Clone, E: Eq + Hash + Clone, S: BuildHasher,

type ValidationError = InvalidFinCategory<E>

The type of a validation error.

fn validate(&self) -> Result<(), NonEmpty<Self::ValidationError>>

Validates the object.

impl<V, E, S> Eq for FinCategory<V, E, S>

where V: Eq + Hash, E: Eq + Hash, S: BuildHasher,