Struct FpCategory

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

A finitely presented category.

Such a presentation is defined by a finite graph together with a set of path equations. A morphism in the presented category is an equivalence class of paths in the graph, so strictly speaking we work with morphism representatives rather than morphism themselves.

Like the object and morphism generators, the equations are identified by keys. Depending on the application, these could be axiom names or meaningless IDs.

Implementations

impl<V, E, EqKey, S> FpCategory<V, E, EqKey, S>

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

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

Graph of generators of the finitely presented category.

pub fn get_equation(&self, key: &EqKey) -> Option<&PathEq<V, E>>

Get a path equation by key.

pub fn equations(&self) -> impl Iterator<Item = &PathEq<V, E>>

Iterates over path equations in the presentation.

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

Adds an object generator, returning whether it is new.

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

where Iter: 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 make_mor_generator(&mut self, e: E) -> bool

Adds a morphism generator without initializing its (co)domain.

pub fn get_dom(&self, e: &E) -> Option<&V>

Gets the domain of a morphism generator.

pub fn get_cod(&self, e: &E) -> Option<&V>

Gets the codomain of a morphism generator.

pub fn set_dom(&mut self, e: E, v: V) -> Option<V>

Sets the domain of a morphism generator.

pub fn set_cod(&mut self, e: E, v: V) -> Option<V>

Sets the codomain of a morphism generator.

pub fn add_equation(&mut self, key: EqKey, eq: PathEq<V, E>)

Adds a path equation to the presentation.

pub fn is_free(&self) -> bool

Is the category freely generated?

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

Iterates over failures to be a well-defined presentation of a category.

Trait Implementations

impl<V, E, EqKey, S> Category for FpCategory<V, E, EqKey, S>

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

type Ob = V

Type of objects in category.

type Mor = Path<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, path: &Path<V, E>) -> bool

Does the category contain the value as a morphism?

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

Gets the domain of a morphism in the category.

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

Gets the codomain of a morphism in the category.

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

Composes a path of morphisms in the category.

fn compose2(&self, path1: Path<V, E>, path2: Path<V, E>) -> Path<V, E>

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

fn id(&self, x: Self::Ob) -> Self::Mor

Constructs the identity morphism at an object.

impl<V: Clone, E: Clone, EqKey: Clone, S: Clone> Clone for FpCategory<V, E, EqKey, S>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<V: Debug, E: Debug, EqKey: Debug, S: Debug> Debug for FpCategory<V, E, EqKey, S>

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

Formats the value using the given formatter.

impl<V, E, EqKey, S> Default for FpCategory<V, E, EqKey, S>

where S: Default,

fn default() -> Self

Returns the “default value” for a type.

impl<V, E, EqKey, S> FgCategory for FpCategory<V, E, EqKey, S>

where V: Eq + Clone + Hash, E: Eq + Clone + Hash, EqKey: Eq + Clone + Hash, 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, EqKey, S> PartialEq for FpCategory<V, E, EqKey, S>

where V: Eq + Hash, E: Eq + Hash, EqKey: 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, EqKey, S> Validate for FpCategory<V, E, EqKey, S>

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

type ValidationError = InvalidFpCategory<E, EqKey>

The type of a validation error.

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

Validates the object.

impl<V, E, EqKey, S> Eq for FpCategory<V, E, EqKey, S>

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