Bartosz Milewski • 5/16/2026

Profunctor Equipment in Haskell

This article provides a toy implementation of profunctor equipment in Haskell, focusing on category theory concepts like 0-cells, 1-cells (functors and profunctors), and 2-cells (natural transformations). It explains horizontal and vertical composition of cells, profunctor composition via coends, unit cells, and companion/conjoint types (Costar and Star). The content is technical, aimed at programmers familiar with Haskell and advanced type-level programming, and demonstrates how to encode categorical structures using the type system.

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#Haskell #Category Theory #Functor