pub trait VDblCategory {
type Ob: Eq + Clone;
type Arr: Eq + Clone;
type Pro: Eq + Clone;
type Cell: Eq + Clone;
Show 27 methods
// Required methods
fn has_ob(&self, ob: &Self::Ob) -> bool;
fn has_arrow(&self, arr: &Self::Arr) -> bool;
fn has_proarrow(&self, pro: &Self::Pro) -> bool;
fn has_cell(&self, cell: &Self::Cell) -> bool;
fn dom(&self, f: &Self::Arr) -> Self::Ob;
fn cod(&self, f: &Self::Arr) -> Self::Ob;
fn src(&self, m: &Self::Pro) -> Self::Ob;
fn tgt(&self, m: &Self::Pro) -> Self::Ob;
fn cell_dom(&self, cell: &Self::Cell) -> Path<Self::Ob, Self::Pro>;
fn cell_cod(&self, cell: &Self::Cell) -> Self::Pro;
fn cell_src(&self, cell: &Self::Cell) -> Self::Arr;
fn cell_tgt(&self, cell: &Self::Cell) -> Self::Arr;
fn compose(&self, path: Path<Self::Ob, Self::Arr>) -> Self::Arr;
fn compose_cells(
&self,
tree: DblTree<Self::Arr, Self::Pro, Self::Cell>,
) -> Self::Cell;
// Provided methods
fn arity(&self, cell: &Self::Cell) -> usize { ... }
fn compose2(&self, f: Self::Arr, g: Self::Arr) -> Self::Arr { ... }
fn id(&self, x: Self::Ob) -> Self::Arr { ... }
fn compose_cells2(
&self,
αs: impl IntoIterator<Item = Self::Cell>,
β: Self::Cell,
) -> Self::Cell { ... }
fn id_cell(&self, m: Self::Pro) -> Self::Cell { ... }
fn has_composite(&self, path: &Path<Self::Ob, Self::Pro>) -> bool { ... }
fn has_unit(&self, x: &Self::Ob) -> bool { ... }
fn composite_ext(
&self,
path: Path<Self::Ob, Self::Pro>,
) -> Option<Self::Cell> { ... }
fn composite2_ext(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Cell> { ... }
fn composite(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Pro> { ... }
fn composite2(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Pro> { ... }
fn unit_ext(&self, x: Self::Ob) -> Option<Self::Cell> { ... }
fn unit(&self, x: Self::Ob) -> Option<Self::Pro> { ... }
}Expand description
A virtual double category (VDC).
See the module-level docs for background on VDCs.
TODO: The universal property of a composite is not part of the interface.
Required Associated Types§
Required Methods§
Sourcefn has_proarrow(&self, pro: &Self::Pro) -> bool
fn has_proarrow(&self, pro: &Self::Pro) -> bool
Does the proarrow belong to the VDC?
Sourcefn cell_dom(&self, cell: &Self::Cell) -> Path<Self::Ob, Self::Pro>
fn cell_dom(&self, cell: &Self::Cell) -> Path<Self::Ob, Self::Pro>
Gets the domain of a cell, a path of proarrows.
Sourcefn cell_cod(&self, cell: &Self::Cell) -> Self::Pro
fn cell_cod(&self, cell: &Self::Cell) -> Self::Pro
Gets the codomain of a cell, a single proarrow.
Provided Methods§
Sourcefn arity(&self, cell: &Self::Cell) -> usize
fn arity(&self, cell: &Self::Cell) -> usize
Gets the arity of a cell.
The default implementation returns the length of the cell’s domain.
Sourcefn compose2(&self, f: Self::Arr, g: Self::Arr) -> Self::Arr
fn compose2(&self, f: Self::Arr, g: Self::Arr) -> Self::Arr
Composes a pair of arrows with compatible (co)domains.
Sourcefn compose_cells2(
&self,
αs: impl IntoIterator<Item = Self::Cell>,
β: Self::Cell,
) -> Self::Cell
fn compose_cells2( &self, αs: impl IntoIterator<Item = Self::Cell>, β: Self::Cell, ) -> Self::Cell
Composes a two-layer pasting of cells.
Sourcefn has_composite(&self, path: &Path<Self::Ob, Self::Pro>) -> bool
fn has_composite(&self, path: &Path<Self::Ob, Self::Pro>) -> bool
Does the path of proarrows have a chosen composite?
The default implementation checks whether composite
returns something.
Sourcefn has_unit(&self, x: &Self::Ob) -> bool
fn has_unit(&self, x: &Self::Ob) -> bool
Does the object have a chosen unit?
The default implementation checks whether unit returns
something.
Sourcefn composite_ext(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Cell>
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.
Such a cell is called an **extension or opcartesian cell.
The default implementation handles the one special kind of composite that always exist: unary composites.
Sourcefn composite2_ext(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Cell>
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.
Sourcefn composite(&self, path: Path<Self::Ob, Self::Pro>) -> Option<Self::Pro>
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.
Sourcefn composite2(&self, m: Self::Pro, n: Self::Pro) -> Option<Self::Pro>
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.
Dyn Compatibility§
This trait is not dyn compatible.
In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.