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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Synthetic category theory SemesterWiSe 2025 / 26 Lecturer Denis-Charles Cisinski Type of course (Veranstaltungsart) Vorlesung Contents Synthetic category theory is a new a logic that serve as foundations of mathematics, in which the notion of (higher) category is the ground concept. This also means that this is the language of higher category theory, as used in modern algebraic topology and algebraic geometry. The formal approach is useful in the sense that it gives new tools to organize the discourse (in particular, proofs) and yields new interpretations right away: many statements do not only hold for usual (higher) category theory but for sheaves of such things as well. This is thus a way to learn higher category theory through what we can do with them, as opposed to how we can build them within classical set theoretic foundations. The goal of this lecture series is to introduce this language formally and to explain its main underlying principles. From there, two directions will be developed:-the theory of presentable categories;-algebraic K-theory. Literature
Recommended previous knowledge Prerequisites: since we will give an axiomatic approach, starting from scratch, there are no other prerequisites than a basic knowledge of category theory (Yoneda Lemma, (co)limits, adjunctions).However, this is an advanced course and we will assume a certain level of maturity, mathematically speaking. Time/Date Tuesday and Thursday 10-12 h Location Tuesday in M102, Thursday in M101 Registration BV, MV, MArGeo, MGAGeo, LA-GyGeo ECTS 9 |