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Derived functors and cohomology through higher categories SemesterWiSe 2021 / 22 Lecturer Denis-Charles Cisinski Type of course (Veranstaltungsart) Vorlesung German title Abgeleiteten Funktoren und Kohomologie durch höheren Kategorien Contents The aim of the course is at first to relate classical constructions of homotopy theory and homological algebra to the ones from infinity-category theory. In particular, we will see how to enhance the axioms of Eilenberg and Steenrod for singular homology theory, or to interpret sheaf cohomology. More generaly, we will see how to interpret any constructions from the theory of Quillen's theory of model categories. Many of the constructions/computations will be an illustration of the theory of Kan extensions in the context of higher categories. In particular, we will see how the concept of Kan extension is fundamental for the organization of mathematical discourse as well as for implementing basic computational tools. This is a natural continuation of the lectures on Higher Categories, but, for students willing to accept basic facts, this is also an oportunity to learn higher categories from examples, through what they do, and we will try our best to make the lecture accessible to an audience as wide as possible. Leitfaden:
Literature Recommended previous knowledge Basics of Algebraic Topology, of Homological Algebra, and of Category Theory Time/Date Mo 16-18, Fri 16-18 Location M 103 or online Course homepage http://www.mathematik.uni-regensburg.de/cisinski/lehre.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MArGeo, MGAGeo, LA-GyGeo ECTS 9 |