pub trait Category {
type Ob: Eq + Clone;
type Mor: Eq + Clone;
// Required methods
fn has_ob(&self, x: &Self::Ob) -> bool;
fn has_mor(&self, f: &Self::Mor) -> bool;
fn dom(&self, f: &Self::Mor) -> Self::Ob;
fn cod(&self, f: &Self::Mor) -> Self::Ob;
fn compose(&self, path: Path<Self::Ob, Self::Mor>) -> Self::Mor;
// Provided methods
fn compose2(&self, f: Self::Mor, g: Self::Mor) -> Self::Mor { ... }
fn id(&self, x: Self::Ob) -> Self::Mor { ... }
}Expand description
A category.
We take the unbiased view of categories, meaning that composition is an operation on paths of arbitrary finite length. This has several advantages. First, it takes as primitive the natural data structure for morphisms in a free category, or more generally in a presentation of a category. It also enables more intelligent strategies for evaluating composites in specific categories. For instance, when composing (multiplying) a sequence of matrices, it can be very inefficient to just fold from the left or right, compared to multiplying in the optimal order.