Main

catlog::dbl::category::WalkingFunctor

Struct Main

pub struct Main();

Expand description

Struct representing the walking functor.

Trait Implementations§

impl VDCWithComposites for Main

fn composite_ext(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Cell>

Gets the chosen cell witnessing a composite of proarrows, if there is one. Read more

fn through_composite( &self, cell: Self::Cell, range: Range<usize>, ) -> Option<Self::Cell>

Factorizes a cell through a composite of proarrows. Read more

fn has_composite(&self, path: &Path<Self::Ob, Self::Pro>) -> bool

Does the path of proarrows have a chosen composite? Read more

fn has_unit(&self, x: &Self::Ob) -> bool

Does the object have a chosen unit? Read more

fn composite2_ext(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Cell>

Gets the chosen cell witnessing a composite of two proarrows, if there is one.

fn composite(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Pro>

Gets the chosen composite for a path of proarrows, if there is one. Read more

fn composite2(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Pro>

Gets the chosen composite for a pair of consecutive proarrows, if there is one.

fn unit_ext(&self, x: Self::Ob) -> Option<Self::Cell>

Gets the chosen extension cell for an object, if there is one. Read more

fn unit(&self, x: Self::Ob) -> Option<Self::Pro>

Gets the chosen unit for an object, if there is one. Read more

fn unit_arrow(&self, f: Self::Arr) -> Option<Self::Cell>

Constructs the unit cell on an arrow, if there is one. Read more

fn through_unit(&self, cell: Self::Cell, index: usize) -> Option<Self::Cell>

Factorizes a cell through the unit proarrow for an object. Read more

impl VDblCategory for Main

type Ob = Ob

Type of objects in the VDC.

type Arr = Arr

Type of arrows (tight morphisms) in the VDC.

type Pro = Ob

Type of proarrows (loose morphisms) in the VDC.

type Cell = Cell

Type of cells in the VDC.

fn has_ob(&self, _: &Self::Ob) -> bool

Does the object belong to the VDC?

fn has_arrow(&self, _: &Self::Arr) -> bool

Does the arrow belong to the VDC?

fn has_proarrow(&self, _: &Self::Pro) -> bool

Does the proarrow belong to the VDC?

fn has_cell(&self, _: &Self::Cell) -> bool

Does the cell belong to the VDC?

fn dom(&self, f: &Self::Arr) -> Self::Ob

Gets the domain of an arrow.

fn cod(&self, f: &Self::Arr) -> Self::Ob

Gets the codomain of an arrow.

fn src(&self, m: &Self::Pro) -> Self::Ob

Gets the source of a proarrow.

fn tgt(&self, m: &Self::Pro) -> Self::Ob

Gets the target of a proarrow.

fn cell_dom(&self, cell: &Self::Cell) -> Path<Self::Ob, Self::Pro>

Gets the domain of a cell, a path of proarrows.

fn cell_cod(&self, cell: &Self::Cell) -> Self::Pro

Gets the codomain of a cell, a single proarrow.

fn cell_src(&self, cell: &Self::Cell) -> Self::Arr

Gets the source of a cell, an arrow.

fn cell_tgt(&self, cell: &Self::Cell) -> Self::Arr

Gets the target of a cell, an edge.

fn compose(&self, path: Path<Self::Ob, Self::Arr>) -> Self::Arr

Composes a path of arrows in the VDC.

fn compose_cells( &self, tree: DblTree<Self::Arr, Self::Pro, Self::Cell>, ) -> Self::Cell

Composes a tree of cells in the VDC.

fn arity(&self, cell: &Self::Cell) -> usize

Gets the arity of a cell. Read more

fn compose2(&self, f: Self::Arr, g: Self::Arr) -> Self::Arr

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

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

Constructs the identity arrow at an object.

fn compose_cells2( &self, αs: impl IntoIterator<Item = Self::Cell>, β: Self::Cell, ) -> Self::Cell
where Self: Sized,

Composes a two-layer pasting of cells.

fn id_cell(&self, m: Self::Pro) -> Self::Cell

Constructs the identity cell on a proarrow.

Auto Trait Implementations§

impl Freeze for Main

impl RefUnwindSafe for Main

impl Send for Main

impl Sync for Main

impl Unpin for Main

impl UnwindSafe for Main

Blanket Implementations§

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

fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

impl<T> Borrow<T> for T
where T: ?Sized,

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

impl<T> BorrowMut<T> for T
where T: ?Sized,

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

Mutably borrows from an owned value. Read more

impl<T> From<T> for T

fn from(t: T) -> T

Returns the argument unchanged.

impl<T> Instrument for T

fn instrument(self, span: Span) -> Instrumented<Self>

Instruments this type with the provided [Span], returning an Instrumented wrapper. Read more

fn in_current_span(self) -> Instrumented<Self>

Instruments this type with the current Span, returning an Instrumented wrapper. Read more

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

fn into(self) -> U

Calls U::from(self).

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

impl<T> IntoEither for T

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

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

impl<T> Pointable for T

const ALIGN: usize

The alignment of pointer.

type Init = T

The type for initializers.

unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more

unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more

unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more

unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more

impl<T> Same for T

type Output = T

Should always be Self

impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).

fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.

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

type Error = Infallible

The type returned in the event of a conversion error.

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.

impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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

The type returned in the event of a conversion error.

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.

impl<V, T> VZip<V> for T
where V: MultiLane<T>,

fn vzip(self) -> V

impl<T> WithSubscriber for T

fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self>
where S: Into<Dispatch>,

Attaches the provided Subscriber to this type, returning a [WithDispatch] wrapper. Read more

fn with_current_subscriber(self) -> WithDispatch<Self>

Attaches the current default Subscriber to this type, returning a [WithDispatch] wrapper. Read more