4 ms·

To say it explicitly, string diagrams are nice exactly because they convert category theoretic equivalences into topological equivalences that are easy to read

by tel 2y ago

To say it explicitly, string diagrams are nice exactly because they convert category theoretic equivalences into topological equivalences that are easy to read visually.

carapace 2y ago
Thanks for trying. I feel like either I've gotten really stupid recently (always a possibility) or maybe this paper is not very good at explaining string diagrams. :(
- tel 2y ago
  String diagrams are also pretty confusing if you're not already very comfortable with category theory. They exist to make complex equality proofs a little easier, but the underlying proofs themselves are not easy to follow.
  - carapace 2y ago
    Yeah, that's a factor here, I'm not very good at CT. (It's weird. It seems so simple, but when you actually get into the weeds things are flying around and morphing and it all falls apart (for me.)) Again, thanks for trying, I really appreciate it. I'll study CT and take another run at it. :)
    - tel 2y ago
      For sure, string diagrams are meant as a tool for someone experienced with category theoretic proofs. It's possible that they could be used in introductory material too--a la that quantum book that's very diagrammatic--but this paper isn't it. Category theory is kind of funny in that it is very simple at its base, but rapidly advances from there. Its greatest strength is how compositional it is, but that also means that most practitioners rapidly begin composing things at many levels of abstraction and it can get tough to follow. String diagrams technically help with that. They have their own compositional rules which map to the ways category theoretic constructions compose, but they still look "simple" to the reader and can provide insight. But in all cases, you need to be comfortable working each component all the way through to fully grasp what's going on. And that can be pretty complex!
      - carapace 2y ago
        Yeah, so much this. Thank you again. :)

by tel 2y ago

To say it explicitly, string diagrams are nice exactly because they convert category theoretic equivalences into topological equivalences that are easy to read visually.

carapace 2y ago

Thanks for trying. I feel like either I've gotten really stupid recently (always a possibility) or maybe this paper is not very good at explaining string diagrams. :(

tel 2y ago
String diagrams are also pretty confusing if you're not already very comfortable with category theory. They exist to make complex equality proofs a little easier, but the underlying proofs themselves are not easy to follow.
- carapace 2y ago
  Yeah, that's a factor here, I'm not very good at CT. (It's weird. It seems so simple, but when you actually get into the weeds things are flying around and morphing and it all falls apart (for me.)) Again, thanks for trying, I really appreciate it. I'll study CT and take another run at it. :)
  - tel 2y ago
    For sure, string diagrams are meant as a tool for someone experienced with category theoretic proofs. It's possible that they could be used in introductory material too--a la that quantum book that's very diagrammatic--but this paper isn't it. Category theory is kind of funny in that it is very simple at its base, but rapidly advances from there. Its greatest strength is how compositional it is, but that also means that most practitioners rapidly begin composing things at many levels of abstraction and it can get tough to follow. String diagrams technically help with that. They have their own compositional rules which map to the ways category theoretic constructions compose, but they still look "simple" to the reader and can provide insight. But in all cases, you need to be comfortable working each component all the way through to fully grasp what's going on. And that can be pretty complex!
    - carapace 2y ago
      Yeah, so much this. Thank you again. :)