Struct FreeVDblCategory

#[repr(transparent)]
pub struct FreeVDblCategory<G: VDblGraph>(pub G);

The VDC freely generated by a virtual double graph.

A virtual double graph freely generated a virtual double category, generalizing how a graph freely generates a category. This is not, however, the most general way to freely generate a VDC. A “virtual double computad” freely generates a VDC but allows the generating cells to have sources and targets that are paths of generating arrows.

Tuple Fields

0: G

Trait Implementations

impl<G: VDblGraph> From<G> for FreeVDblCategory<G>

fn from(value: G) -> Self

Converts to this type from the input type.

impl<G: VDblGraph> RefCast for FreeVDblCategory<G>

type From = G

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

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

impl<G: VDblGraph> VDblCategory for FreeVDblCategory<G>

where G::ProE: Debug,

type Ob = <G as VDblGraph>::V

Type of objects in the VDC.

type Arr = Path<<G as VDblGraph>::V, <G as VDblGraph>::E>

Type of arrows (tight morphisms) in the VDC.

type Pro = <G as VDblGraph>::ProE

Type of proarrows (loose morphisms) in the VDC.

type Cell = DblTree<<G as VDblGraph>::E, <G as VDblGraph>::ProE, <G as VDblGraph>::Sq>

Type of cells in the VDC;

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

Does the object belong to the VDC?

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

Does the arrow belong to the VDC?

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

Does the proarrow belong to the VDC?

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

Does the cell belong to the VDC?

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

Gets the domain of an arrow.

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

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

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

Gets the codomain of a cell, a single proarrow.

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

Gets the source of a cell, an arrow.

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

Gets the target of a cell, an edge.

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

Gets the arity of a cell.

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 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

Composes a two-layer pasting of cells.

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

Constructs the identity cell on a proarrow.

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

Does the path of proarrows have a chosen composite?

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

Does the object have a chosen unit?

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.

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.

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.

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

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