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?
Speakers
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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