What's the thing with category theory? I see this topic discussed quite frequently here but I don't get it why people are so into it
For me.. It's a very useful mental model for thinking about architecture & logic
Category Theory Illustrated – Natural Transformations
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Re: Category Theory Illustrated – Natural Transformations
#12Re: Category Theory Illustrated – Natural Transformations
#13What's the thing with category theory? I see this topic discussed quite frequently here but I don't get it why people are so into it
It's just a good set of models to use to think about all sorts of different mathematical systems, kind of like a unified vocabulary. Beyond undergraduate level, category theory these days plays a huge role within many vast fields - e.g., algebraic geometry, algebraic topology, or representation theory.
Re: Category Theory Illustrated – Natural Transformations
#14Re: Category Theory Illustrated – Natural Transformations
#15When I read this title I thought it was going to be rings and groups in bikinis. I’m so dumb.
Re: Category Theory Illustrated – Natural Transformations
#16Earlier quoted context omitted.
For me.. It's a very useful mental model for thinking about architecture & logic
Why not simply use UML?
UML doesn't give ideas for how to actually structure things. Category theory is primarily a theory of nice ways things can be put together or form relationships while maintaining invariants.
Re: Category Theory Illustrated – Natural Transformations
#17What's the thing with category theory? I see this topic discussed quite frequently here but I don't get it why people are so into it
Category theory is what you get when you take mappings instead of sets as the primitive objects of your universe. At first this might seem a perverse thing to do as mappings seem more complex than sets, but that is just because traditionally mappings have usually been defined in terms of sets.
In set theory you can specify that two sets be equal and you can also specify that one set be an element of another.
In category theory you can specify that two mappings be equal and you can also specify that two mappings compose end to end to produce a third mapping.
Category theory can be used to express some requirements in a very concise way.
Re: Category Theory Illustrated – Natural Transformations
#18Had to reduce the page to 67% to get out of "Fisher Price" font size, but otherwise quite interesting.
Re: Category Theory Illustrated – Natural Transformations
#19What's the thing with category theory? I see this topic discussed quite frequently here but I don't get it why people are so into it
Category theory is what you get when you take mappings instead of sets as the primitive objects of your universe. At first this might seem a perverse thing to do as mappings seem more complex than sets, but that is just because traditionally mappings have usually been defined in terms of sets. In set theory you can specify that two sets be equal and you can also specify that one set be an element of another. In categ…
> Category theory can be used to express some requirements in a very concise way.
Can you an example?
Re: Category Theory Illustrated – Natural Transformations
#20What's the thing with category theory? I see this topic discussed quite frequently here but I don't get it why people are so into it
It's just a good set of models to use to think about all sorts of different mathematical systems, kind of like a unified vocabulary. Beyond undergraduate level, category theory these days plays a huge role within many vast fields - e.g., algebraic geometry, algebraic topology, or representation theory.
I think your reply overstates the importance of category theory in mathematics and doesn't give any hint on what it is about.
IMO a better reply would be: category theory appeared to unify the concepts around using discrete objects to prove the properties of continous objects in topology, like fundamental groups, homology groups and homothopy groups. It is only practically useful for very advanced proofs like 2nd Weil Conjecture. Any usage of it in programming is only an analogy and is not mathematically rigorous (see https://math.andrej.com/2016/08/06/hask-is-not-a-category/)