# Tabulation Tribulations

DevFeed: [Tabulation Tribulations](<https://devfeed.tech/articles/tabulation-tribulations-28858.md>)

Original publisher: [Read original article](<https://bartoszmilewski.com/2026/05/23/tabulation-tribulations/>)

Author: Bartosz Milewski

Published: 2026-05-23T16:05:49Z

Content type: article

Language: en

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

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [category-theory](<https://devfeed.tech/tags/category-theory.md>), [double-categories](<https://devfeed.tech/tags/double-categories.md>), [graph](<https://devfeed.tech/tags/graph.md>), [mapping](<https://devfeed.tech/tags/mapping.md>), [object](<https://devfeed.tech/tags/object.md>), [pairs](<https://devfeed.tech/tags/pairs.md>), [profunctor-equipment](<https://devfeed.tech/tags/profunctor-equipment.md>), [profunctors](<https://devfeed.tech/tags/profunctors.md>)

## AI overview

This article explains tabulations in double categories by relating them to graphs of functions, relations, and profunctors. It describes the category of elements of a profunctor and introduces tabulation through projections and a universal property, including conditions for morphisms and 2-cells.

## Source excerpt

Previously: Bending, Yanking, and Cartesian Squares in Double Categories. We all know what a graph of a function is: it's a set of pairs , where . Similarly, a graph of a relation is a set of pairs where is related to . A profunctor can be viewed as a proof-relevant relation. So a graph [...]