3 ms·
> for some reason I don't think just sets are sufficient The reason you're looking for is that the category of sets is not a set.
by mydogcanpurr 4y ago
> for some reason I don't think just sets are sufficient
The reason you're looking for is that the category of sets is not a set.
- vishal0123 4y agoWhile category of sets technically could not be expressed as a ZFC set, the idea behind the set theory is enough. Also you could add an axiom[0] in ZFC to make category of set a set. [0]: https://en.wikipedia.org/wiki/Grothendieck_universe https://en.wikipedia.org/wiki/Grothendieck_universe
- ginnungagap 4y agoThis is routinely dealt with through Grothendieck universes. Those are a fancy name for what is pretty much an inaccessible level of the cumulative hierarchy, indeed ZFC+"every set belongs to a Grothendieck universe" is equiconsistent with ZFC+"there is a proper class of inaccessible cardinals". This is not a strong assumption over pure ZFC compared to those set theorists interested in large cardinals work with