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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

Location: Kräftriket Hus 6, Rum 306 (SU)

Participating: Peter LeFanu Lumsdaine

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Full details at course web page


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


  • (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