HomSetX

HomSetX is a software toolkit for category theory research and education that concentrates on the computation and exploration of Hom-sets between objects in mathematical categories. It provides an interactive environment to define categories, objects, and morphisms, and to compute Hom(A,B), the set of morphisms from A to B. The project supports finite and finitely presented categories and can model certain enriched structures and 2-categories.

Overview and development: The project began as an open-source initiative in the early 2020s and is maintained by a community of contributors from academia and software development. It is cross-platform and designed to integrate with other computational algebra systems, with bindings for Python and interfaces to systems such as SageMath.

Key features: HomSetX includes data models for objects and morphisms, and an engine for computing Hom-sets, along with support for composition, identities, and basic diagrammatic reasoning. It provides tools for calculating limits and colimits where feasible, as well as memoization and caching to improve performance. The toolkit exposes a Python API, with JSON import/export and lightweight visualization of morphisms and their relationships.

Architecture and usage: The project adopts a modular architecture consisting of a core solver, a category-definition layer, and a user-facing API. Categories can be described by generators and relations, or by explicit lists of objects and morphisms. The engine emphasizes finite exploration and offers options for tracing the construction or existence of morphisms.

Access and licensing: HomSetX is released under a permissive open-source license and hosted on a public repository, with documentation and tutorials for both beginners and researchers.

See also: Hom-set, category theory, computational category theory.