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vpatryshev/Categories

Here we do all categorical calculations, for small (aka, embeddable fully into a program) categories
Source code at GitHub null
vpatryshev/Categories.json
{
  "createdAt": "2015-05-31T21:36:36Z",
  "defaultBranch": "master",
  "description": "Here we do all categorical calculations, for small (aka, embeddable fully into a program) categories",
  "fullName": "vpatryshev/Categories",
  "homepage": null,
  "language": "Scala",
  "name": "Categories",
  "pushedAt": "2025-06-25T23:36:53Z",
  "stargazersCount": 25,
  "topics": [],
  "updatedAt": "2025-06-08T21:08:39Z",
  "url": "https://github.com/vpatryshev/Categories"
}

Categories Project

Section titled “Categories Project”

Intro

Section titled “Intro”

This is a Scala implementation of category theory calculations and topos logic (and topologies). Historically, it was first written in Basic, then in Fortran, then in Assembler, then in Java, now in Scala. Long story.

The idea is to be able to do all categorical calculations, then be able to calculate topos logic and topologies.

A bunch of slide sets can be found here:

Current Status

Section titled “Current Status”

Everything works, but has too many .asInstanceOf[] injected, will have to get rid of them eventually.

What we have now:

  • sets (including infinite and finite sets, including ZFC and the set of Natural Numbers)
  • graphs (directed multigraphs, actually)
  • categories, with parsers in the form like val W = category"({a,b,c,d,e}, {ab: a -> b, cb: c -> b, cd: c -> d, ed: e -> d})"
  • initial and terminal objects in categories, products of categories, degreees
  • functors, cones, cocones, limits, colimits
  • set diagrams, that is, functors with a set category as a codomain
  • diagrams (that’s set diagrams) (presheaves)
  • subterminals
  • points
  • representable functors
  • (lattice of) subobjects
  • build subobject classifiers,
  • define Heyting trait (challenging, with generalized points),
  • build logic,
  • table of logic on points,
  • svg rendering of categories (see samples.html)
  • classifying arrow
  • Lawvere topologies

WIP:

  • Scala 3

Plans:

  • sheaves
  • pullback in a topos

TODO: use this trick: https://gist.github.com/non/51b83d0abc929cc4f0b153accf2bf02f