Learn · Category theory
Axeyum for category theorists
Axeyum offers a clear experiment in adding abstraction above independently constructed carriers and measured trust boundaries.
a103b3db3 Measured Source Axeyum fact ledger and implementation documentation After reading this guide, you should be able to
Learning objectives
- Identify the parts of Axeyum that are relevant to category theory.
- Distinguish implemented results from the current research frontier.
- Open a lesson or artifact that provides the underlying definitions and evidence.
Current state
Can a concrete-carrier library grow a useful abstraction layer?
The formal library was built from concrete natural, integer, rational, real, complex, and geometric carriers. A hierarchy of algebraic structure records now sits above those constructions. Categories, functors, natural transformations, and universal properties form the next abstraction layer.
That order of construction makes the abstraction problem unusually visible. A future categorical layer must recover reusable structure from existing concrete proofs without concealing their algorithms, assumptions, or axiom footprints.
Why it matters
What the current work makes possible
- The carrier-first corpus supplies many nontrivial examples for testing abstraction.
- Every proposed abstraction can be judged by how many existing results it actually unifies.
- The ledger can record whether transport through an abstraction changes the trusted surface.
Results to inspect
Open the evidence
What comes next
Extend the present base
The first layer is categories, functors, natural transformations, products, and universal properties for structures already present in the library.
A successful layer should reduce duplicate proofs while preserving executable definitions and readable dependency edges. That gives the project a concrete measure of whether the abstraction scales.
Where to begin