Natural Transformations: Coherent Change Across Systems
When you change from one architecture to another, changes must be consistent everywhere. Part 6 of applying category theory to Solutions Architecture—the mathematics of coherent transformation.
🏷️ Category Theory
9 posts tagged with Category Theory
Functors: The Mathematics of Migration
Every migration is a functor — a structure - preserving transformation between systems. Part 5 of applying category theory to Solutions Architecture, where we learn when migrations succeed and why they fail.
Composition as Architectural Law: Diagnosing Integration Failures
When services don't compose, it's not a bug—it's a mathematical impossibility. Part 4 of applying category theory to Solutions Architecture, where we develop a diagnostic framework for integration failures.
The Yoneda Perspective: Systems Defined by Their Interfaces
A system is completely characterized by how other systems interact with it. Part 3 of applying category theory to Solutions Architecture—the deepest insight in category theory, made practical.
Equivalence of Categories: When Different Architectures Are 'The Same'
A monolith and microservices can be mathematically equivalent. Part 7 of applying category theory to Solutions Architecture—understanding when radically different implementations are categorically identical.
Morphisms All the Way Down: API Design as Arrow-First Thinking
Stop designing services. Start designing contracts. Part 2 of applying category theory to Solutions Architecture—where we learn that the arrows, not the boxes, are the architecture.
The Categorical Solutions Architect: Viewing Architecture Through the Lens of Category Theory
Category theory isn't abstract nonsense—it's the formal language for the problems Solutions Architects already face. Part 1 of a series on applying mathematical foundations to real architectural challenges.
Categories of the Commons: Formalizing Open Source Governance with Mathematics
Announcing my MBA thesis research: applying category theory, sheaf cohomology, and cybernetics to understand why some open source projects thrive while others collapse. Can we predict governance crises before they happen?
Category Theory for JavaScript/TypeScript Developers
From Bartosz Milewski's Haskell-centric approach to something tailored for the JS/TS ecosystem. Exploring adjunctions, monads, and why Promise.then() is actually category theory in disguise.
