Higher categories study group

Venue: HIM lecture hall, Poppelsdorfer Allee 45
Organizer: Marco Castronovo

For those who were interested in learning about higher categories, a study group started on Wednesday, May 13th, from 9 a.m. to 12 noon at the HIM lecture hall.

The plan was to understand a survey of Moritz Groth on ∞-categories (pdf). Familiarity with category theory and simplicial sets was assumed. There were talks and discussions afterwards.

TALK 1 May 13. Daniela Egas (MPIM Bonn)

  • Kan complexes as model for (∞,0)-categories
  • quasi-categories as model for (∞,1)-categories
  • homotopy category of a q.c.
  • mapping space of 2 objects in a q.c.

TALK 2 May 18. Dominic Culver (Notre Dame)

  • C q.c. and X s.s. ⇒ CX q.c.
  • contractibility of compositional choices in a q.c.
  • q.c. are the fibrant objects in Joyal model structure
  • equivalence and weak equivalence of q.c.

TALK 3 May 20. Mark Penney (Oxford)

  • simplicially enriched category of a s.s.
  • homotopy coherent nerve
  • combinatorial description of s.e. categories via necklaces
  • many homotopy coherent nerves are q.c.

TALK 4 May 22. Jeremy Mann (Notre Dame)

  • initial object of a q.c.
  • join of q.c.
  • slice q.c.
  • colimits in q.c.

TALK 5 May 29. Manuel Araujo (Oxford)

  • Grothendieck opfibrations and Segal condition
  • coCartesian fibrations of q.c.
  • symmetric monoidal ∞-categories and functors
  • algebra objects

TALK 6 June 22. Shan Shah (Utrecht) & Hiro Tanaka (Harvard)

  • Dold-Kan correspondence
  • dg nerve
  • Fukaya categories