Introduction to Infinity-Categories

This reading group have finished.

The goal of this reading group is to introduce the basic notions of infinity-categories in the model of quasicategories and make the participants comfortable with how the foundations are built, and how to carry out proofs in this language. This will be done by going through 4 important theorems: Joyal's lifting theorem, Straightning-Unstraightning, the Yoneda lemma and the Adjoint Functor theorem. The main reference will be Markus Lands book "Introduction to Infinity-categories".

Below is an overview of the talks, and here is a more detailed description.

Talk 1 (05.10 - MS.05) Introduction: Paul Pantea - Notes

Talk 2 (12.10 - C1.06 ) Small object argument and internal hom: Daniel Marlowe - Notes

Talk 3 (19.10 - C1.06) Joyal's lifting theorem: David Tintinago Pinzon

Talk 4 (26.10) Localization and coCartesian fibrations: Tommy Yang - Notes

Talk 5 (02.11) Straightening-Unstraightening: Thomas Read - Notes

Talk 6 (09.11) Colimits and Yoneda: Dhruva Divate

Talk 7 (16.11) Adjoint functors: Sunny Sood

Talk 8 (23.11) Adjoint functor theorem: Hannah MacDermott - Notes

Talk 9 (30.11) Stable infinity-categories: Julie Rasmusen - Notes

Talk 10 (07.12) Infinity-operads: Julie Rasmusen - Notes