Category Theory Explained for Haskell Programmers – Part 1 | Jencel Panic | ZuriHac 2026

Jencel Panic introduces category theory for functional programmers, moving from sets and functions to categories, morphisms, and universal properties.

What is category theory, and why does it matter for functional programming? In Part 1, Jencel Panic builds an intuitive introduction from sets and functions to categories, morphisms, products, coproducts, and universal properties, with practical connections to Haskell throughout. Starting from basic set theory, the talk revisits familiar concepts such as subsets, singleton sets, the empty set, functions, identity functions, and function composition before gradually building toward the categorical viewpoint used throughout modern mathematics and programming language theory. A central theme is the shift from internal descriptions, which focus on elements inside sets, to external descriptions based on relationships between objects. Using diagrams and commuting diagrams, Jencel demonstrates how concepts such as composition, associativity, and isomorphism can be expressed entirely through arrows and their properties. The session explores products and coproducts, connecting mathematical definitions with practical programming concepts such as tuples, records, and the Either type in Haskell. Through universal properties, the talk shows how these structures can be characterized by the functions associated with them rather than by their internal implementation. The presentation also introduces categorical descriptions of singleton and empty sets, explaining initial and terminal objects and demonstrating how set elements themselves can be represented categorically. By the end, viewers gain a foundation for understanding categories, morphisms, identity, associativity, isomorphisms, universal properties, products, coproducts, and duality. Chapters 00:00:00 Introduction And Motivation 00:02:26 Set Theory Foundations 00:04:44 Functions In Set Theory 00:06:17 Empty Sets And Singleton Sets 00:07:52 Hom-Sets And External Diagrams 00:11:09 Function Composition And Engineering 00:15:06 Commuting Diagrams 00:20:12 Associativity Of Composition 00:21:00 Isomorphisms And Categories 00:26:00 Products And Tuples 00:31:11 Universal Property Of Products 00:38:49 Coproducts And Either Types 00:43:33 Categorical Definitions 00:45:08 Elements Through Morphisms 00:49:01 Initial And Terminal Objects 00:50:57 Applying Functions Categorically 00:53:02 Defining Categories 00:58:25 Categories, Types, And Morphisms About the Speaker Jencel is a writer turned programmer. They are the author of the book Category Theory Illustrated. Jencel Panic presented this talk at ZuriHac 2026, held at OST – Eastern Switzerland University of Applied Sciences in Rapperswil-Jona, Switzerland. Jencel was introduced by Farhad Mehta. ZuriHac is one of the largest community events for Haskell and functional programming and is organized by Zürich Friends of Haskell (ZFOH) together with OST. OST article: ost.ch/en/details/news/zurihac-2026-1 Zürich Friends of Haskell: zfoh.ch/ ZuriHac 2026: zfoh.ch/zurihac2026/ #ZuriHac #Haskell #functionalprogramm