Struct ResGraphMorphism 

pub struct ResGraphMorphism<S: ResGraphObject, T: ResGraphObject> {
    pub mapping: HashMap<usize, usize>,
    /* private fields */
}

A morphism in the ResGraph category

A morphism f: A → B is a graph homomorphism that:

• Maps vertices of A to vertices of B
• Preserves adjacency: if v~w in A, then f(v)~f(w) in B
• Preserves resonance structure (compatibility with E₈)

Type Parameters

• S - Source object type
• T - Target object type

The phantom types ensure type safety: you can only compose morphisms where the target of the first equals the source of the second.

Fields

mapping: HashMap<usize, usize>

Vertex mapping: source vertex → target vertex

Implementations

impl<S: ResGraphObject, T: ResGraphObject> ResGraphMorphism<S, T>

pub const fn new(mapping: HashMap<usize, usize>) -> Self

Create a new morphism from a vertex mapping

Arguments

• mapping - Maps source vertices to target vertices

Returns

A new morphism (unchecked - caller must ensure adjacency preservation)

pub fn identity(object: &S) -> ResGraphMorphism<S, S>

Create the identity morphism for an object

The identity morphism id_A: A → A maps each vertex to itself.

Arguments

• object - The ResGraph object

Returns

The identity morphism id: A → A

pub fn apply(&self, vertex: usize) -> Option<usize>

Apply this morphism to a vertex

Arguments

• vertex - Source vertex index

Returns

The target vertex, or None if not in domain

pub fn num_vertices(&self) -> usize

Get the number of vertices in the source

pub fn compose<U: ResGraphObject>( &self, next: &ResGraphMorphism<T, U>, ) -> ResGraphMorphism<S, U>

Compose two morphisms: self ∘ other

Given f: A → B (self) and g: B → C (next), computes g ∘ f: A → C

Mathematically: (g ∘ f)(v) = g(f(v))

Arguments

• next - The morphism to compose after this one

Returns

The composite morphism

Trait Implementations

impl<S: Clone + ResGraphObject, T: Clone + ResGraphObject> Clone for ResGraphMorphism<S, T>

fn clone(&self) -> ResGraphMorphism<S, T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<S: Debug + ResGraphObject, T: Debug + ResGraphObject> Debug for ResGraphMorphism<S, T>

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

Formats the value using the given formatter.