Category-Theory

Duality: The Hidden Structure of Opposites

Many structures come in pairs: forward/reverse AD, push/pull iteration, encode/decode. Recognizing duality lets you transfer theorems and insights between domains.

Category Theory for Programmers

Cipher Maps: A Unified Framework for Oblivious Function Approximation Through Algebraic Structures and Bernoulli Models

Cipher Maps: When Category Theory Meets Oblivious Computing

What if we could compute on encrypted data while preserving algebraic structure? Not through expensive homomorphic encryption, but through a principled mathematical framework that unifies oblivious computing, Bernoulli types, and categorical …

Algebraic Cipher Types: A Functorial Framework for Secure Computation

Algebraic Cipher Types: Computing on Encrypted Data While Preserving Structure

A functorial framework that lifts algebraic structures into the encrypted domain, enabling secure computation that preserves mathematical properties.

The Dot Ecosystem: From Simple Paths to Data Algebras

A mathematically grounded ecosystem of composable tools for manipulating nested data structures. From simple helper functions to sophisticated data algebras, guided by purity, pedagogy, and the principle of least power.