# Kan Extensions in Haskell

DevFeed: [Kan Extensions in Haskell](<https://devfeed.tech/articles/kan-extensions-in-haskell-28859.md>)

Original publisher: [Read original article](<https://bartoszmilewski.com/2026/06/08/kan-extensions-in-haskell/>)

Author: Bartosz Milewski

Published: 2026-06-08T12:31:58Z

Content type: tutorial

Language: en

Sources: [Bartosz Milewski's Programming Cafe](<https://devfeed.tech/sources/bartosz-milewski-s-programming-cafe.md>)

Topics: [Haskell](<https://devfeed.tech/topics/haskell.md>), [Reflex FRP](<https://devfeed.tech/topics/reflex-frp.md>)

Tags: [building](<https://devfeed.tech/tags/building.md>), [category-theory](<https://devfeed.tech/tags/category-theory.md>), [extensions](<https://devfeed.tech/tags/extensions.md>), [haskell](<https://devfeed.tech/tags/haskell.md>), [kan-extensions](<https://devfeed.tech/tags/kan-extensions.md>), [programming](<https://devfeed.tech/tags/programming.md>), [types](<https://devfeed.tech/tags/types.md>), [universal-arrows](<https://devfeed.tech/tags/universal-arrows.md>)

## AI overview

This article explains Kan extensions in category theory and translates their definitions and constructions into Haskell. It focuses on right Kan extensions, adjunctions, universal arrows, and pointwise constructions.

## Source excerpt

Previously: Tabulation Tribulations. If you think of functor composition as a form of multiplication, Kan extensions are an attempt to construct inverses of this multiplication. But unlike multiplication, composition is not symmetric, so we have extensions that attempt to undo precomposition, and lifts that do the same for postcomposition. Furthermore, there rarely is a single [...]