most recent 30 from http://mathoverflow.net 2013-05-19T03:15:29Z http://mathoverflow.net/feeds/question/115099 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/115099/are-grothendieck-universes-enough-for-the-foundations-of-category-theory Mozibur Ullah 2012-12-01T19:23:44Z 2012-12-01T22:53:46Z

<p>Grothendieck universes are equivalent to ZFC+a strongly inaccessible cardinal. This is low on the large cardinal axiom list. Is it enough to place category theory on a firm foundational basis, and how about higher category theory, does it remain enough?</p>

http://mathoverflow.net/questions/115099/are-grothendieck-universes-enough-for-the-foundations-of-category-theory/115105#115105 Fred Rohrer 2012-12-01T20:28:57Z 2012-12-01T20:28:57Z

<p>I suggest you have a look at Grothendieck's SGA 4, Exposé I, where a lot of category theory is developed (and applied) on the basis of Bourbaki set theory plus Grothendieck's axioms UA and UB about universes.</p>

http://mathoverflow.net/questions/115099/are-grothendieck-universes-enough-for-the-foundations-of-category-theory/115123#115123 Daniel Schäppi 2012-12-01T22:37:55Z 2012-12-01T22:53:46Z

<p>Mike Shulman wrote a nice expository paper on set theoretical foundations for category theory</p> <p><a href="http://arxiv.org/abs/0810.1279" rel="nofollow">http://arxiv.org/abs/0810.1279</a></p> <p>In Section 6 he explains the difficulties of working with large categories using just ZFC, and he discusses various ways to deal with these size issues. Some of these do not assume the existence of an inaccessible cardinal.</p>