A friendly introduction to infinity-categories

The aim of these lectures is to answer the question: What do we really mean by "spaces", and what do we want to do with them?

schedule Date & time
Date/time
31 Jan 2022 | 4 - 5pm
3 Feb 2022 | 4 - 5pm
7 Feb 2022 | 4 - 5pm
10 Feb 2022 | 4 - 5pm
14 Feb 2022 | 4 - 5pm
17 Feb 2022 | 4 - 5pm
person Speaker

Speakers

Yuki Maehara, Kyushu University, Japan
contact_support Contact
Yoshihiro Maruyama

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Description

To join this seminar via Zoom please click here.

If you would like to join the seminar and are not currently affiliated with ANU, please contact Yoshihiro Maruyama.

Infinity-categories are to spaces what ordinary categories are to sets. This nicely summarises the basic idea of infinity-categories, but there is a large gap between this intuition and the definition(s) of infinity-category one finds in the literature. The aim of these lectures is to fill this gap by answering the following question: What do we really mean by "spaces", and what sort of things do we want to do with them?

Lecture Plan

Lecture 1: Homotopy groups and Whitehead's theorem 

Lecture 2: Kan complexes

Lecture 3: Model categories

Lecture 4: Homotopy commutative vs homotopy coherent

Lecture 5: Quasi-categories via spines

Lecture 6: Quasi-categories via inner horns

Location

Online