Struct DiscreteDblTheory

pub struct DiscreteDblTheory<Cat: FgCategory>(/* private fields */);

A discrete double theory.

A discrete double theory is a double theory with no nontrivial operations on either object or morphism types. Viewed as a double category, such a theory is indeed discrete, which can equivalently be defined as

• a discrete object in the 2-category of double categories
• a double category whose underlying categories are both discrete categories

Trait Implementations

impl<Cat: Debug + FgCategory> Debug for DiscreteDblTheory<Cat>

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

Formats the value using the given formatter.

impl<Cat: FgCategory> From<Cat> for DiscreteDblTheory<Cat>

fn from(value: Cat) -> Self

Converts to this type from the input type.

impl<Cat: FgCategory> RefCast for DiscreteDblTheory<Cat>

type From = Cat

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

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

impl<C: FgCategory> VDCWithComposites for DiscreteDblTheory<C>

where C::Ob: Clone, C::Mor: Clone,

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

In a discrete double theory, every cell is an extension.

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

Factorizes a cell through a composite of proarrows.

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 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 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.

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

Factorizes a cell through the unit proarrow for an object.

impl<C: FgCategory> VDblCategory for DiscreteDblTheory<C>

where C::Ob: Clone, C::Mor: Clone,

type Ob = <C as Category>::Ob

Type of objects in the VDC.

type Arr = <C as Category>::Ob

Type of arrows (tight morphisms) in the VDC.

type Pro = <C as Category>::Mor

Type of proarrows (loose morphisms) in the VDC.

type Cell = Path<<C as Category>::Ob, <C as Category>::Mor>

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, arr: &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, path: &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, path: &Self::Cell) -> Path<Self::Ob, Self::Pro>

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

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

Gets the codomain of a cell, a single proarrow.

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

Gets the source of a cell, an arrow.

fn cell_tgt(&self, path: &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.

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.

impl<C: FgCategory + Validate> Validate for DiscreteDblTheory<C>

type ValidationError = <C as Validate>::ValidationError

The type of a validation error.

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

Validates the object.