报告人：叶凌远

题目：Categories Are the Right Land for (Mathematical) Logic

时间：2021/4/13 15:10-18:00

地点：二教416

摘要：This talk will consist of two parts. To make it as self-contained as possible, I will familiarize you with the basic language of category theory, including the definitions of categories, functors and natural transformations, in the first half of this talk. I will also try to make a few philosophical remarks that show you why categorical thinking might be fruitful and how it relates to logic. In the second half, I will talk about categorical semantics of a logic and the notion of syntactic category of a theory. Using these notions and constructions, I will (i) show you how categorical semantics has broaden the application of logic to a great extent, (ii) provide you a proof of a strong completeness result, and (iii) talk about the duality between syntax and semantics. Due to (category-theory-related) technical reasons, the second half will mainly focus on algebraic theories, but if time permitted I will say some words about how these notions and constructions generalize to several different fragments of first-order theories as well. The frontier of the current research of categorical logic in general involves quite sophisticated mathematics, but is also mathematically very powerful. I consider this talk as a first step towards convincing you that category theory in general is the right place to do (mathematical) logic.