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Because you cannot discard more detail than what CT has chosen to discard. You start with objects and arrows, and how the arrows compose. Every object has an id
by proc0 9y ago
Because you cannot discard more detail than what CT has chosen to discard. You start with objects and arrows, and how the arrows compose. Every object has an identity which is another arrow, so in some sense you have just a composition of arrows, and that's it. CT starts really simple, and I don't think there's anything left to hide or abstract.
- Koshkin 9y agoYou may be wrong here, there have been some discussions - see for example https://www.quora.com/Whats-more-general-than-category-theory https://www.quora.com/Whats-more-general-than-category-theor...
- mbid 9y agoEvery category is an infinity category, but the converse is not true. Thus, infinity categories are more general than categories. But you don't have to go that far: Just remove e.g. identity morphisms from categories, and you get something that is more general than categories. It is of course another matter completely whether these structures are a useful abstraction for what you want to accomplish. I've never come across something reasonable that has arrows and associative composition, but no identities. As for infinity categories, I remain very skeptical that they abstract any problems programmers not concerned with topology (i.e. > 99%) have. So yeah, categories are a reasonable baseline from where you can build. But you can't show anything relevant and non-trivial that holds in any category. You'll need more structure, hence less generality, for that.