For me this lacked a clear motivation; why category theory? Seems with number and set theory examples I can just use those existing tools/theories to do what you're doing. There is a massive jump at the end about how to apply it some ways but without any clear justification, e.g. why would a data scientist or AI person think this can help them?
One of the motivations for category for me was when I subscribed to a thesis that Analogy is the core of cognition, in a Douglas Hofstadter sense. Category theory can be thought of as the language of Analogy, being the language of structure. So applying CT in that area seems like it will be very useful. David Spivak has also written about what is called 'ontology logs', ologs. Which can be helpful with knowledge representation. I think of it as the start of a formalized mind map.
In the field of deep learning, you can think of parameters or layer as an main category. By using the category analogy, it helps me to clarify my thought concise. The theory provide some thought framework like, what would be the functor or monad if I think of the parameter is ‘a dot’?
Thanks for the upload. I don't think I've ever seen the puzzles at 35:10 before.
Thank you. That was helpful to me. I’m curious about CT. I bought the Mac Lane book but soon got lost.
to Math is human; to Cat, divine
For me this lacked a clear motivation; why category theory? Seems with number and set theory examples I can just use those existing tools/theories to do what you're doing. There is a massive jump at the end about how to apply it some ways but without any clear justification, e.g. why would a data scientist or AI person think this can help them?
Can someone knowledgeable please respond to this? It would be very helpful to me
One of the motivations for category for me was when I subscribed to a thesis that Analogy is the core of cognition, in a Douglas Hofstadter sense. Category theory can be thought of as the language of Analogy, being the language of structure. So applying CT in that area seems like it will be very useful.
David Spivak has also written about what is called 'ontology logs', ologs. Which can be helpful with knowledge representation. I think of it as the start of a formalized mind map.
th-cam.com/video/bk36__qkhrk/w-d-xo.html Perhaps this presentation will motivate the topic.
It is the key to understand mathematics for programmers who don’t understand mathematics
In the field of deep learning, you can think of parameters or layer as an main category. By using the category analogy, it helps me to clarify my thought concise. The theory provide some thought framework like, what would be the functor or monad if I think of the parameter is ‘a dot’?