Classical Category Theory in Plain Scala

on YouTube ↗32m

" summary

Scala code implements a full implementation of small categories (objects, arrows, identities, composition), graphs, functors, natural transformations, cones and algorithms to search for limits and colimits, with unit tests exercising finite cases. It provides a Zermelo-Fraenkel model with Choice inside Scala via a BigSet abstraction (sets by predicate, enumerable vs non-enumerable) and represents diagrams as functors; some constructions are decidable and tested for finite domains while others may not exist or be non-enumerable. Repo on GitHub holds the working code.

AI-written summary · about

" chapters (9)

1. 0:00Introduction to category theory
2. 2:21Tiny categories in Scala
3. 8:11Big set category
4. 15:28Functors between categories
5. 19:28Natural transformations
6. 21:45Limits and cones
7. 26:31Diagrams and applications
8. 28:59Practical uses and future plans
9. 30:09Q&A session

" related talks

• 52mCategory Theory Through Functional Programming (part 1/3)Alejandro Serrano · LambdaConf Winter Retreat 2017
• 41mA Pragmatic Introduction to Category TheoryDaniela Sfregola · Lambda World 2017
• 42mA pragmatic introduction to Category TheoryDaniela Sfregola · Scala Days Berlin 2018
• 40mA Pragmatic Introduction to Category TheoriesDaniela Sfregola · Code Mesh 2017
• 02h 24mCategory Theory TrackRichard Southwell · ZuriHac 2025
• 56mCalculating Intuitionistic Logic in ScalaVlad Patryshev · LambdaConf 2019
• 57mApplied category theory and abstract algebraGabriel Gonzales · LambdaConf Winter Retreat 2017
• 42mWhat did category theory do for us?Sergei Winitzki · Scale By The Bay 2019