FunctorFlow.jl

FunctorFlow.jl is a Julia package for building AI systems as categorical diagrams. It provides:

• a typed diagram DSL for objects, morphisms, Kan extensions, and obstruction losses
• a backend-neutral execution pipeline
• Lux-backed neural compilation for trainable architectures
• categorical extensions for universal constructions, causal semantics, sheaves, coalgebra, and JEPA-style world models

FunctorFlow.jl is a Julia port of the original Python FunctorFlow package by Sridhar Mahadevan, and extends it with a Julia-native macro DSL, Lux integration, and tighter interoperability with the AlgebraicJulia ecosystem.

Documentation map

• Getting Started: installation, a first diagram, and macro syntax
• Core Concepts: the package model of diagrams, Kan extensions, losses, and execution
• Block Library: prebuilt categorical building blocks and training-oriented Lux helpers
• Vignettes: rendered tutorial notebooks and longer worked examples
• API Reference: reference pages for the exported API

Package highlights

FunctorFlow centers on a small set of primitives:

• Diagram for architecture specification
• FFObject, Morphism, KanExtension, and ObstructionLoss for categorical structure
• compile_to_callable for backend-neutral execution
• compile_to_lux for differentiable execution with Lux
• @functorflow and Unicode operators like Σ, Δ, and → for concise authoring

For longer worked examples, see the published Vignettes page.