Higher category lecture

A series of introductory lectures on higher categories will be given online by Yuki Maehara, starting on 31 Jan (Mon), then every Mon and Thu, and finishing on 17 Feb (Thu), as per below.

Title: A friendly introduction to ∞-categories

Lecturer: Yuki Maehara (Kyushu U)

Abstract: ∞-categories are to spaces what ordinary categories are to sets. This nicely summarises the basic idea of ∞-categories, but there is a large gap between this intuition and the definition(s) of ∞-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?

Slides available at:

https://drive.google.com/drive/folders/1yl--ANYq3svswH0yc-ZIJXHD6WMY7VN7

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

Schedule:

31 Jan (Mon) 4-5pm (AEDT/GMT+11)

3 Feb (Thu) 4-5pm (AEDT/GMT+11)

7 Feb (Mon) 4-5pm (AEDT/GMT+11)

10 Feb (Thu) 4-5pm (AEDT/GMT+11)

14 Feb (Mon) 4-5pm (AEDT/GMT+11)

17 Feb (Thu) 4-5pm (AEDT/GMT+11)

Held online via zoom webinar at:

https://anu.zoom.us/j/87221396938?pwd=azgxQmJWWWhtTUFHUGdpcXE2MGp6QT09

No registration required.

Organisers:

Yoshihiro Maruyama and Florrie Verity (Australian National University)

Contact: yoshihiro.maruyama@anu.edu.au and florrie.verity@anu.edu.au