I attended the seminar of category theory. Although it began at 8:45, I slept in till noon. Actually I had woke up at eight but then I got back to sleep...orz. Anyway I arrived at past 2:00.
Today's first topic was diagonal arguments. Cantor's diagonal arguments were generalized to Lawvere's diagonal theorem which is also called Lawvere's fixpoint theorem. The theorem is related to the works of Russel, Gödel and Tarski. The theorem was very interesting but we couldn't understand Lawvere's arguments about ‘idealization’. The next topic was map objects (expontiation). In exercises we had to prove certain isomorphisms like YT×S≅(YT)S. The calculation was tiresome, but we could prove them by using the uniqueness property of map objects.
After the seminar we went to さくら水産.
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