catlog::one::category

Struct DiscreteCategory

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pub struct DiscreteCategory<S: Set>(/* private fields */);
Expand description

The discrete category on a set.

The objects of the category are the elements of the set, and the only morphisms are the identities, which can thus be identified with the objects.

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impl<S: Set> Category for DiscreteCategory<S>

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type Ob = <S as Set>::Elem

Type of objects in category.
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type Mor = <S as Set>::Elem

Type of morphisms in category.
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fn has_ob(&self, x: &S::Elem) -> bool

Does the category contain the value as an object?
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fn has_mor(&self, f: &S::Elem) -> bool

Does the category contain the value as a morphism?
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fn dom(&self, x: &S::Elem) -> S::Elem

Gets the domain of a morphism in the category.
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fn cod(&self, x: &S::Elem) -> S::Elem

Gets the codomain of a morphism in the category.
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fn compose(&self, path: Path<S::Elem, S::Elem>) -> S::Elem

Composes a path of morphisms in the category.
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fn compose2(&self, f: Self::Mor, g: Self::Mor) -> Self::Mor

Composes a pair of morphisms with compatible (co)domains.
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fn id(&self, x: Self::Ob) -> Self::Mor

Constructs the identity morphism at an object.
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impl<S: FinSet> FgCategory for DiscreteCategory<S>

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type ObGen = <S as Set>::Elem

Type of an object generator. Read more
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type MorGen = <S as Set>::Elem

Type of a morphism generator Read more
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fn ob_generators(&self) -> impl Iterator<Item = Self::ObGen>

Iterates over object generators.
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fn mor_generators(&self) -> impl Iterator<Item = Self::MorGen>

Iterates over morphism generators.
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fn mor_generator_dom(&self, f: &Self::MorGen) -> Self::Ob

The domain of a morphism generator
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fn mor_generator_cod(&self, f: &Self::MorGen) -> Self::Ob

The codomain of a morphism generator
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fn objects(&self) -> impl Iterator<Item = Self::Ob>

Iterates over basic objects.
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fn morphisms(&self) -> impl Iterator<Item = Self::Mor>

Iterates over basic morphisms.
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impl<S: Set> From<S> for DiscreteCategory<S>

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fn from(value: S) -> Self

Converts to this type from the input type.
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impl<S: Set> RefCast for DiscreteCategory<S>

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type From = S

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fn ref_cast(_from: &Self::From) -> &Self

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fn ref_cast_mut(_from: &mut Self::From) -> &mut Self

Auto Trait Implementations§

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impl<S> Freeze for DiscreteCategory<S>
where S: Freeze,

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impl<S> RefUnwindSafe for DiscreteCategory<S>
where S: RefUnwindSafe,

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impl<S> Send for DiscreteCategory<S>
where S: Send,

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impl<S> Sync for DiscreteCategory<S>
where S: Sync,

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impl<S> Unpin for DiscreteCategory<S>
where S: Unpin,

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impl<S> UnwindSafe for DiscreteCategory<S>
where S: UnwindSafe,

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.