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Category Theory is a controversial topicsubfield of Mathematics studying mathematical structures and their conservation through various transformation. It emerged in it's usefulness. it can perhaps be described as an attempt to create a language of generalizations
So you’ve heard of this thing called “category theory”. Maybe you’ve met some smart people who say that’s it’s really useful and powerful for… something. Maybe you’ve even cracked open a book or watched some lectures, only to find thattheentire subject seems to have been generated by trainingGPT-2on a mixstudy of algebraicoptometrytopology, then went on to apply to most parts of mathematics.Despite some work on applied category theory, it's usefulness for problem solving (especially in topics close to LW, such as Rationality and
output fromtheproofistrivial.comAI Safety.(from here)
note: i (the person who wrote the current description) knows very little about) is still controversial. One possible explanation is that category theory usually comes after the results, to structure them and made it because it's a fitting topic and cluster of posts, so someone should look over this and fix what may need fixing (and then delete this note)find the links with previous results in other fields.
Category Theory is a controversial topic in it's usefulness. it can perhaps be described as an attempt to create a language of generalizations
So you’ve heard of this thing called “category theory”. Maybe you’ve met some smart people who say that’s it’s really useful and powerful for… something. Maybe you’ve even cracked open a book or watched some lectures, only to find that the entire subject seems to have been generated by training GPT-2 on a mix of algebraic optometry and output from theproofistrivial.com. (from here)
note: i (the person who wrote the current description) knows very little about category theory and made it because it's a fitting topic and cluster of posts, so someone should look over this and fix what may need fixing (and then delete this note)
Category Theory is a subfield of
Mathematicspure mathematics studyingmathematical structuresany structure that contains objects and theirconservation through various transformation.relations (referred to as morphisms). It emerged in the study of algebraictopology,topology, then went on to apply beyond mathematics and into various scientific disciplines, a metamathematical framework comparable tomost partsthat ofmathematics.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.Despite some workCurrent research on applied category theory, it's usefulnessand Categories forproblem solving (especially inAI are useful and relevant for topics close to LW, such as Rationalityand, AI Safety) is still controversial. One possible explanation is that, and Game theory. Due to its abstract nature, category theoryusually comes afteris jokingly criticized as being "abstract nonsense". A major theorem result is Yoneda embedding, which is basically theresults, to structure them and find the links with previous results in other fields.idea that an object can be defined by its all of its relations.