# PhD course: infinity-categories (organisational meeting)

Initial organisational meeting for HT19 PhD course on infinity categories, lecturer Peter LeFanu Lumsdaine.

**Time: **
Thu 2019-09-12 14.00

**Lecturer: **
Peter LeFanu Lumsdaine

**Location: ** Kräftriket Hus 6, Rum 306 (SU)

Full details at course web page

### Outline:

Infinity-categories arose as a tool of homotopy theory, and have become essential tools in large parts of the subject today; they have also turned out to be significant in logic, as semantics for various forms of dependent type theory. In this course, I will aim to:

- introduce the basic notions of infinity-categories, taking quasi-categories as a model, and the standard homotopy-theoretic examples as motivation;
- develop their basic “category theory”, using the approach of Riehl–Verity;
- “infinity categories as models of homotopy theory”: show how abstract homotopy theory can be developed in suitable infinity-categories, up to the richest setting, infinity toposes;
- “infinity-categorical logic”: introduce the language of dependent type theory, and show how it can be used formally and heuristically as a internal language for suitable infinity-categories

### Prerequisites:

- (essential) basic core category theory
- (helpful) some background in homotopy theory, especially simplicial sets and/or categorical methods
- (helpful) some background in logic, especially type theory and/or categorical logic