19234201

SoSe 17: Categories and Homotopy Theory

Daniela Egas Santander

Zusätzl. Angaben / Voraussetzungen

ATTENTION!
Because of scheduling problems and because this course is a follow up of Lecture 19215101 "Topologie III" by Elmar Vogt the dates of the two lectures will be as follows:

Both courses run on Tu 12-14, SR 031/A7 and Th 12-14, SR 140/A7(Hinterhaus)
Topologie III starts on 18.04. 2017 and ENDS on 01.06.2017;
Categories and Homotopy Theory STARTS on 06.06.2017 and ends on 20.07.2017.

The contents of both lectures are basic for (algebraic and geometric) topology, and we strongly recommend for students to take both as a single package.

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Kommentar

This course is a follow up of Lecture 19215101 "Topologie III" by Elmar Vogt and STARTS on 06.06.2017. The contents of both lectures are basic for (algebraic and geometric) topology, and we strongly recommend for students to take both as a single package.

Exercises are conducted by Filipp Levikov and run as scheduled to cover both courses.

CONTENTS of Categories and homotopy theory:

This will be an introduction to some of the basic techniques of homotopy theory that use category theory. We will cover basic categorical constructions: functors, adjunctions, monads, the yoneda lemma, (co) limits and we use these to describe the category of simplicial sets. We go back to homotopy theory with the concept of model categories, homotopy (co) limits. One of our main goals is to understand Quillen's Theorem A and why simplicial sets are combinatorial models for spaces. This course will complement the reading seminar in infinity categories 19233511.

For the content of "Topologie III" go to Lecture 19215101 in KVV or eVV.

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