Nodal decomposition
In category theory, an abstract mathematical discipline, a nodal decomposition of a morphism φ : X → Y {\displaystyle \varphi :X\to Y} is a representation of φ {\displaystyle \varphi } as a product φ = σ ∘ β ∘ π {\displaystyle \varphi =\sigma \circ \beta \circ \pi } , where π {\displaystyle \pi } is a strong epimorphism, β {\displaystyle \beta } a bimorphism, and σ {\displaystyle \sigma } a strong monomorphism. == Uniqueness and notations == If it exists, the nodal decomposition is unique up to an isomorphism in the following sense: for any two nodal decompositions φ = σ ∘ β ∘ π {\displaystyle \varphi =\sigma \circ \beta \circ \pi } and φ = σ ′ ∘ β ′ ∘ π ′ {\displaystyle \varphi =\sigma '\circ \beta '\circ \pi '} there exist isomorphisms η {\displaystyle \eta } and θ {\displaystyle \theta } such that π ′ = η ∘ π , {\displaystyle \pi '=\eta \circ \pi ,} β = θ ∘ β ′ ∘ η , {\displaystyle \beta =\theta \circ \beta '\circ \eta ,} σ ′ = σ ∘ θ .