Coursebooks

Higher Categories: Theory and Practice

MATH-637

Lecturer(s) :

Rasekh Nima

Language:

English

Frequency

Only this year

Remarque

from 1.3.-1.5.2020

Summary

The goal of this course is to familiarize students with the theory and application of $(\infty,1)$-categories. The theory includes introducing various models and the presenting the fibrational approach. Practice includes an application to the students primary interest.

Content

The content breaks down into two parts:
 
Theoretical Part:
Introducing various models of $(\infty,1)$-categories, concrete Kan enriched categories, quasi-categories and complete Segal spaces.
Discussing their respective model structures and how to translate between them.
Introducing fibrations of quasi-categories: Right fibrations and Cartesian fibrations.
Defining limits and colimits using fibrations. Proving standard results about limits using the language of fibrations
 
Practical Part:
This part is not predetermined and depends on the students who attend the first part.
We will cover some of application of higher category theory to parts of mathematics that is of the interest to the students that attended the first part.

Keywords

Models of $(\infty,1)$-categories, Cartesian fibrations, Applications of higher category theory

Learning Prerequisites

Required courses

Some familiarity with category theory and homotopy theory

Learning Outcomes

By the end of the course, the student must be able to:

Resources

Notes/Handbook

There will be lecture notes for this course. We will partially rely on following material:

In the programs

    • Semester
    • Exam form
       Oral
    • Credits
      2
    • Subject examined
      Higher Categories: Theory and Practice
    • Lecture
      16 Hour(s)
    • Practical work
      14 Hour(s)

Reference week

 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German