catex-jc

Experiments with category theory.

A Java library for experimenting with category-theoretic concepts in software modeling. Supports representation of a domain-specific data structure as a (finite) category via user implementation of the CategorySource interface. The category-theoretic representation can then be used to reason and gain insight about the underlying data structure and it's properties; how it might relate to mathematical structures such as graphs, posets, or lattices; and to render and visualize the data as SVG diagrams.

Features

• Create a finite category with objects, morphisms, and a composition table
• Validate category laws (identity, associativity, unit laws)
• Convert categories to graphs, partial orders, lattices, and Hasse diagrams
• Render any structure to SVG with customizable layouts and styles

Requirements

• Java 17+
• Gradle (provided via wrapper)

Dependencies

Library	Version	License	Purpose
JGraphT	1.5.2	LGPL 2.1 / EPL 2.0	Directed graph implementation

Building

./gradlew build

Testing

./gradlew test

Usage

Define a category

Implement CategorySource on your domain object and provide it as a FiniteCategory:

var category = myDomain.toCategory();
category.validate(); // checks identity and associativity laws

Convert to other structures

Use the fluent CategoryConverter facade:

// To a directed graph
DirectedGraph<L> graph = CategoryConverter.from(category).toGraph();

// To a partial order (requires a preorder category)
PartialOrder<L> poset = CategoryConverter.from(category).toPoset();

// To a lattice (requires a preorder lattice category)
Lattice<L> lattice = CategoryConverter.from(category).toLattice();

// To a Hasse diagram
HasseDiagram<L> hasse = CategoryConverter.from(category).toHasseDiagram();

Render to SVG

var renderer = new HasseDiagramRenderer<>();
renderer.renderSvgToFile(hasse, Path.of("output.svg"));

Customize the output with RenderOptions:

RenderOptions opts = RenderOptions.builder()
    .width(1000).height(700)
    .nodeColor("#4A90D9")
    .labelColor("#FFFFFF")
    .fontSize(14)
    .layerHeight(120)
    .build();

renderer.renderSvgToFile(hasse, Path.of("output.svg"), opts);

Renderers are available for all structures: CategoryRenderer, GraphRenderer, LatticeRenderer, HasseDiagramRenderer.

Package Structure

Package	Description
com.github.catexjc.core	FiniteCategory, CategoryObject, Morphism, CategorySource
com.github.catexjc.convert	CategoryConverter — unified conversion facade
com.github.catexjc.graph	DirectedGraph, GraphConverter
com.github.catexjc.poset	PartialOrder, PosetConverter
com.github.catexjc.lattice	Lattice, LatticeConverter
com.github.catexjc.hasse	HasseDiagram, HasseDiagramConverter
com.github.catexjc.render	Renderers, RenderOptions, SVG layout internals

Notes

• All data structures are immutable.
• Category law validation is lazy — call validate() explicitly.
• Conversions to poset/lattice/Hasse diagram require a preorder category (at most one morphism between any two objects). An IllegalArgumentException is thrown if the category does not meet the required properties.