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: Category Theory Meets Oblivious Computing

Formalizing oblivious computing through cipher maps and algebraic cipher types, using category theory for functorial composition of privacy-preserving transformations.

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 composable ecosystem of tools for manipulating nested data structures. From a simple helper function to a full data algebra, guided by purity, pedagogy, and the principle of least power.