Cat­e­gory Theory

TagLast edit: 22 Jan 2024 13:23 UTC by MIN0010

Category Theory is a subfield of pure mathematics studying any structure that contains objects and their relations (referred to as morphisms). It emerged in the study of algebraic topology, then went on to apply beyond mathematics and into various scientific disciplines, a metamathematical framework comparable to that of type theory and set theory. The notion of compositionality is what differs category theory from graph theory, in which the nodes themselves can be categories.

Current research on applied category theory and Categories for AI are useful and relevant for topics close to LW, such as Rationality, AI Safety, and Game theory. Due to its abstract nature, category theory is jokingly criticized as being “abstract nonsense”. A major theorem result is Yoneda embedding, which is basically the idea that an object can be defined by its all of its relations.

Towards Hodge-podge Alignment

Cleo Nardo19 Dec 2022 20:12 UTC
91 points
30 comments9 min readLW link

Cat­e­gories: mod­els of models

countedblessings9 Oct 2019 2:45 UTC
52 points
18 comments12 min readLW link

In­tro­duc­tion to In­tro­duc­tion to Cat­e­gory Theory

countedblessings6 Oct 2019 14:43 UTC
112 points
19 comments2 min readLW link

Mul­ti­plica­tive Oper­a­tions on Carte­sian Frames

Scott Garrabrant3 Nov 2020 19:27 UTC
34 points
24 comments12 min readLW link

Cat­e­gory The­ory Without The Baggage

johnswentworth3 Feb 2020 20:03 UTC
125 points
49 comments13 min readLW link

Carte­sian frames as gen­er­al­ised models

Stuart_Armstrong16 Feb 2021 16:09 UTC
20 points
0 comments5 min readLW link

Ex­am­in­ing Arm­strong’s cat­e­gory of gen­er­al­ized models

Morgan_Rogers10 May 2022 9:07 UTC
14 points
0 comments7 min readLW link

CTWTB: Paths of Com­pu­ta­tion State

johnswentworth8 Sep 2020 20:44 UTC
40 points
1 comment4 min readLW link

Uncer­tainty in all its flavours

Cleo Nardo9 Jan 2024 16:21 UTC
25 points
6 comments35 min readLW link

Ad­di­tive Oper­a­tions on Carte­sian Frames

Scott Garrabrant26 Oct 2020 15:12 UTC
62 points
6 comments11 min readLW link

Biex­ten­sional Equivalence

Scott Garrabrant28 Oct 2020 14:07 UTC
43 points
13 comments10 min readLW link

Cat­e­gor­i­cal-mea­sure-the­o­retic ap­proach to op­ti­mal poli­cies tend­ing to seek power

jacek12 Jan 2023 0:32 UTC
31 points
3 comments6 min readLW link

Finite Fac­tored Sets to Bayes Nets Part 2

J Bostock3 Feb 2024 12:25 UTC
6 points
0 comments8 min readLW link

Ab­strac­tions as mor­phisms be­tween (co)algebras

Erik Jenner14 Jan 2023 1:51 UTC
17 points
1 comment8 min readLW link

Semi-Sim­pli­cial Types, Part I: Mo­ti­va­tion and History

astradiol9 Mar 2024 22:07 UTC
20 points
3 comments10 min readLW link

Davi­dad’s Bold Plan for Align­ment: An In-Depth Explanation

19 Apr 2023 16:09 UTC
154 points
29 comments21 min readLW link

What is cat­e­gory the­ory?

countedblessings6 Oct 2019 14:33 UTC
64 points
6 comments3 min readLW link

[Question] Why does cat­e­gory the­ory ex­ist?

Ben Pace25 Apr 2019 4:54 UTC
37 points
10 comments1 min readLW link

Roadmap for a col­lab­o­ra­tive pro­to­type of an Open Agency Architecture

Deger Turan10 May 2023 17:41 UTC
30 points
0 comments12 min readLW link

The sen­tence struc­ture of mathematics

countedblessings7 Oct 2019 18:58 UTC
41 points
15 comments2 min readLW link

Ex­am­ples of Categories

countedblessings10 Oct 2019 1:25 UTC
27 points
2 comments5 min readLW link

Gen­er­al­ised mod­els as a category

Stuart_Armstrong16 Feb 2021 16:08 UTC
25 points
9 comments4 min readLW link