(I won't promise to pass on specific questions at question time, but I'd be happy to try to condense suggested questions into one or two suitable ones if I can do the necessary processing in real time to make them germane to the actual talk. Always hard to know what to ask in advance of hearing a talk. In any event the lesson of Ireland, Iraq, UACT, etc. is that the TV ads promising that you can learn harmony overnight are to be taken with a grain of salt, it takes a lot of patience. -vp) Dept. of Mathematics Colloquium Thursday April 22, 4:15 PM, Room 380:380W Speaker: Solomon Feferman, Stanford Title: What foundations for category theory? Abstract. Naive category theory leads to certain constructions such as "the category of all categories" and "the category of all functors between two given categories", that border on inconsistency and necessitate consideration of foundations for the subject. Even applications of category theory to homological algebra, for example, raise problems. Two kinds of set-theoretical foundations for category theory have been proposed by Mac Lane and Grothendieck, but each has its drawbacks. In this talk I will describe a more logically sophisticated set-theoretical foundation that improves on these by means of reflective universes. Tea in advance, Bldg. 380 2nd floor lounge.