Struct CrossedModule 

pub struct CrossedModule {
    pub g: FiniteGroup,
    pub h: FiniteGroup,
    pub partial: Vec<usize>,
}

A crossed module ∂: H → G — the algebraic model of a 2-group. partial[h] is ∂(h) ∈ G, a group homomorphism. Its homotopy groups are π₁ = coker(∂) and π₂ = ker(∂).

Fields

g: FiniteGroup

h: FiniteGroup

partial: Vec<usize>

partial[x] = ∂(x) for x ∈ H.

Implementations

impl CrossedModule

pub fn is_homomorphism(&self) -> bool

∂ must be a group homomorphism: ∂(x · y) = ∂(x) · ∂(y).

pub fn pi_two(&self) -> Vec<usize>

π₂ = ker(∂) — the elements of H mapping to the identity of G. The genuine higher homotopy.

pub fn image_size(&self) -> usize

|im(∂)| — the size of ∂’s image in G.

pub fn pi_one_order(&self) -> usize

|π₁| = |coker(∂)| = |G| / |im(∂)| (valid when im(∂) is normal, which holds for our examples).