Notes on linearly distributive categories and applications
This blog intends to be a one-stop, approachable reference for linearly distributive categories, associated structures and applications. The idea is to assimilate the materials on this topic strewn across multiple (a super hard hike-like) papers and provide it in a form that anyone with a basic understanding of category theory, the science of connections and compositions can get a feel for this cool tool!
My introduction to linearly distributive categories happened due to my interest in quantum mechanics. My PhD thesis is on using linearly distributive categories to describe quantum processes and systems of any dimension. I am excited to share more about this as we progress in this blog!
Thanks to Paweł Sobociński for the initial spark and the inspiration to pen this series! This blog is powered by VuePress. Thanks to Daniel Fiłonik for being my personal VuePress ambassador!
Dedication: To Robin Cockett and his 'short' hikes in the Rockies 🏔️
Chapter 1: Linearly distributive categories (LDCs)
Episode 1. Linear logic :Origins of LDCs
Episode 2. Building blocks of linear logic: Linear logic LEGO
Episode 3. Categorical presentation of linear logic :Linear logic through the lens of category theory
Episode 4. From linear logic to quantum mechanics :A reason to care
Episode 5. Linearly distributive categories - Part I :What is linear distributivity?
Episode 6. Linearly distributive categories - Part II :Meet the star of the series!
Episode 7. Versions of LDCs :Compacting LDCs to monoidal categories
Episode 8. The graphical calculus :Drawing the proofs
Episode 9. Linear adjunction and *-autonomous categories :Negation in linear logic = duals in LDCs
Episode 10. Examples of LDCs :Big and small
Chapter 2: Functors and transformations
Content to come 🧑🍳 ...
Chapter 3: Frobenius relations and bialgebras
Content to come 🧑🍳 ...
Chapter 4: Application of LDCs to quantum
Content to come 🧑🍳 ...
Chapter 5: Application of LDCs to concurrency
Content to come 🧑🍳 ...