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Formalization of higher category theory II SemesterSoSe 2024 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 introduced in the previous lecture series 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 now 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 type theory)). Recommended previous knowledge It is recommended to have followed the lecture Formalization of higher category theory. However, for those who would be interested, lecture notes as well as video recordings of the latter can be accessed to on the corresponding GRIPS page: https://elearning.uni-regensburg.de/course/view.php?id=64170 Time/Date Tuesday 16h00-18h00, Thursday 14h00-16h00 Location Tuesday 16h00-18h00 in M 101, Thursday 14h00-16h00 in M102 Registration
BV, MV, MArGeo, MGAGeo, LA-GyGeo ECTS 9 |