IMPRESSUM    DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen. Note For our digital courses all relevant information can be found on the appropriate GRIPS sites. Higher Category Theory Semester WiSe 2020 / 21 Lecturer Denis Charles-Cisinski Type of course (Veranstaltungsart) Vorlesung Contents Higher Categor Theory is the modern approach of Category Theory which includes the contribution of homotopy theory right from the start. This means that the way we identify objects and operators is much more general than equality or isomorphisms. This provides very powerful tools in algebraic topology and in algebraic geometry as well as in more applied areas such as computer science. This lecture, which will continue in the Summer Semester 2021 as well, aims at giving a proper introduction starting from scratch. In particular, no prior knowledge of category theory or of homotopy theory will be needed, and we will carefully state all definitions and give many examples. However, it is strongly recommended to follow a lecture on a related subject, such as Algebraic Topology 1 and/or Cohomology of sheaves 1 in order to build a good supply of non-trivial examples and of beautiful areas of mathematics where to apply the methods of Higher Categor Theory. Literature Denis-Charles Cisinski, Higher Categories and Homotopical algebra, Cambridge studies in advanced mathematics, vol. 180, Cambridge University Press, 2019. Available at http://www.mathematik.uni-regensburg.de/cisinski/CatLR.pdf Jacob Lurie, Higher Topos Theory, Annals of Mathematics Studies, vol. 170, Princeton University Press, 2009. Available at https://www.math.ias.edu/~lurie/papers/HTT.pdf Jacob Lurie, Kerodon https://kerodon.net/ Emily Riehl, Category Theory in Context, Dover Publications, 2016. Available at http://www.math.jhu.edu/~eriehl/context.pdf Emily Riehl, Categorical Homotopy Theory, New Mathematical Monographs, Cambridge University Press, 2014. Available at http://www.math.jhu.edu/~eriehl/cathtpy.pdf Recommended previous knowledge None. But some amount of mathematical maturity and taste for sophisticated tools obtained after a couple years of studies of pure mathematics will certainly help. Time/Date Monday, 14-16h and Friday 14-16h Location digital Course homepage http://www.mathematik.uni-regensburg.de/cisinski/lehre.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration Preliminary registration for the organisation of exercise classes: at the end of the previous semester via EXA or LSF (see announcement by the department) Registration for the exercise classes: via GRIPS, during the first week Registration for course work/examination/ECTS: FlexNow Course work (Studienleistungen) Successful participation in the exercise classes: 50 % of the credits, presentation of asolution in class Examination (Prüfungsleistungen) Oral exam: Duration: 30 min., Date: individual, re-exam: Date: individual Regelungen bei Studienbeginn vor WS 2015 / 16 Benotet: O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung Unbenotet: O. g. Studienleistung Modules BV, MV, MArGeo, MGAGeo, LA-GyGeo ECTS 9

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