Compositefree

Compositefree is a term used in mathematics and computer science to describe a property of an object or system that cannot be expressed as a nontrivial composition of smaller components within a prescribed structure.

In mathematics, compositefree often appears in the context of category theory and modules. A morphism f: A → B is compositefree if there do not exist an object C and morphisms g: A → C and h: C → B with f = h ∘ g where neither g nor h is an identity. Equivalently, an object X is compositefree when it cannot be decomposed as a direct sum of two nonzero subobjects. In this sense, compositefree objects align with the idea of indecomposability. Concrete examples include one-dimensional vector spaces, which are typically compositefree, whereas higher-dimensional spaces can often be decomposed into smaller subspaces.

In computer science and software engineering, compositefree describes a design principle that avoids internal composition of complex structures. A compositefree component or module relies on primitive operations and exposes a stable, minimal interface, with composition occurring only at clearly defined boundaries. This approach can improve testability, maintainability, and reasoning about behavior, at the possible cost of more verbose or explicit wiring of components.

See also: indecomposable, primitive element, direct sum, morphism factorization, design by composition.