250093 VO Introduction to category theory (2015S)
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Details
Sprache: Englisch
Prüfungstermine
Donnerstag
09.07.2015
Mittwoch
22.07.2015
Donnerstag
17.12.2015
Donnerstag
21.01.2016
Dienstag
26.01.2016
Mittwoch
16.03.2016
Mittwoch
06.04.2016
Mittwoch
29.06.2016
Freitag
29.09.2017
Freitag
13.10.2017
Donnerstag
11.01.2018
Freitag
23.11.2018
Freitag
14.12.2018
Freitag
20.11.2020
Lehrende
Termine
Beginn: Donnerstag, 19. März 2015 (später Beginn wegen Connes' Vortrag am 5.3. und Rektorstag am 12.3.)
Schrödinger Lecture Hall im Erwin-Schrödinger-InstitutTermine: Donnerstag 11:15 bis 12:45 UhrInformation
Ziele, Inhalte und Methode der Lehrveranstaltung
This course is an introduction to category theory, a theory of structures and powerful organising principles with many applications. We start with an extended discussion of the basic definitions and properties of categories and functors, with many illustrating and motivating examples from various areas of mathematics.Important milestones of later parts of the lecture course will be the study of universal properties in the following guises: (i) adjoint functors; (ii) representability and the Yoneda lemma; (iii) limits (special cases of which are products, equalisers, or pullbacks) and colimits (e.g. sums, coequalisers, or pushouts).The last part of the course will depend on the audience's taste; possible topics include (a) (co)ends (generalising (co)limits) and Kan extensions; (b) the relation to logic and computer science (lambda calculus and Curry-Howard correspondence), (c) monoidal categories with additional structures (relevant e.g. for topological and conformal field theories), or (d) aspects of "categorification" (e.g. of representations of Lie algebras or of polynomial knot invariants).
Art der Leistungskontrolle und erlaubte Hilfsmittel
oral exams at the end of the course
Mindestanforderungen und Beurteilungsmaßstab
Prüfungsstoff
Literatur
Zuordnung im Vorlesungsverzeichnis
MALV, MGEV
Letzte Änderung: Sa 21.11.2020 00:21