Enum List

pub enum List {
    Plain,
    Symmetric,
    Coproduct,
    Product,
    Biproduct,
}

List modalities available in a modal double theory.

There is just one list, or free monoid, monad on the category of sets, but the double category of sets admits, besides the plain list double monad, a number of variations decorating the spans of lists with extra combinatorial data.

Variants

Plain

Lists of objects and morphisms (of same length).

Symmetric

Lists of objects and morphisms, allowing permutation of the codomain list.

Coproduct

Lists of objects and morphisms, allowing reindexing of the codomain list.

This modality is a skeletized version of the “finite family”, or free finite coproduct completion, construction.

Product

Lists of objects and morphisms, allowing reindexing of the domain list.

This modality is a skeletized version of the free finite product completion.

Biproduct

Lists of objects and morphisms, allowing independent reindexing of both domain and codomain lists.

This modality is a version of the free finite biproduct completion, equivalent to freely enriching in commutative monoids and then applying the matrix construction (Mac Lane, Exercise VIII.2.6) on such an enriched category.

Trait Implementations

impl Clone for List

fn clone(&self) -> List

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for List

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

Formats the value using the given formatter.

impl From<List> for Modality

fn from(value: List) -> Self

Converts to this type from the input type.

impl PartialEq for List

fn eq(&self, other: &List) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for List

impl Eq for List

impl StructuralPartialEq for List