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Formalization of higher category theory SemesterWiSe 2023 / 24 Lecturer Denis-Charles Cisinski Type of course (Veranstaltungsart) Vorlesung Contents This lecture series aims art introducing higher category theory in an axiomatic way. Instead of building the theory of higher category theory from scratch, we will introduce higher category theory formally (in particular very rigorously),with the aim of having access to its main features as quickly as possible: the Yoneda embedding, the straightening/unstraightening correspondence relating cocartesian fibrations with functors taking values in the infinity-category of infinity-categories, the theory of Kan extensions. We will then explore its consequences: the theory of presentable categories, topoi, stable categories, basics on K-theory. Our axiomatic approach will not only provide tools to comprehend the important aspect of higher categories as they are used in practice (derived algebraic geometry, homotopical algebra...) but also in more general contexts (e.g. higher category theory internally in any higher topos) and in logic (dependent typetheory)). 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 16h00-18h00, Thursday 14h00-16h00 Location Tuesday 16h00-18h00 in M 103, Thursday 14h00-16h00 in M102 Registration
BV, MV, MArGeo, MGAGeo, LA-GyGeo ECTS 9 |