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