ColimJ

colimJ is an open-source Java library for computing colimits in category theory. It provides data structures and algorithms for constructing colimits of diagrams in various categories, enabling constructive proofs and computational experiments.

The library focuses on finite diagrams in categories such as Set, Group, and posets, and supports common colimits including coproducts, coequalizers, pushouts, and more complex finite colimits. ColimJ emphasizes the universal property of colimits, offering representations both as cocone objects and as explicit universal maps. It can verify that a proposed cocone satisfies the universal property and, when possible, produce the induced map from the colimit.

Architecture: modular Java library with a generic core that models categories, functors, diagrams, cones and cocones. It provides a diagram builder API, a colimit solver component, and optional adapters for interoperability with other math libraries. Implementations prioritize correctness, with extensive unit tests and property-based tests.

Usage: developers define a diagram, select the target category, and request the colimit; the library returns a colimit object along with the canonical cocone. The API is designed to be language-agnostic within Java, and integrates with Maven/Gradle build systems, with documentation and tutorials available in the project repository.

Impact and reception: colimJ is intended as a practical tool for researchers and educators in category theory, formal verification, and algebraic topology. It supports experimentation with colimit constructions and serves as a teaching aid for universal properties. It is released as open-source software under a permissive license, with ongoing development and community involvement.