Ultraproducts, categorically
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Thu, 16/05 17:00 |
Tom Leinster (Edinburgh) |
Logic Seminar  |
L3 |
| It has long been a challenge to synthesize the complementary insights offered by model theory and category theory. A small fragment of that challenge is to understand ultraproducts categorically. I will show that, granted some general categorical machinery, the notions of ultrafilter and ultraproduct follow inexorably from the notion of finiteness of a set. The machine in question, known as the codensity monad, has existed in an underexploited state for nearly fifty years. To emphasize that it was not constructed specifically for this purpose, I will mention some of its other applications. This talk represents joint work with an anonymous referee. Little knowledge of category theory will be assumed. | |||