Talk: Accessible and Presentable infinity categories

Disclaimer

  • these are supplementary notes for my talk about "Accessible and Presentable infinity categories"
  • I have tried to add more content (especially proofs I will skip)
  • unfortunately my notes contain errors and are not self-sustained

Default Notation

mathematical

  • \(\mu\) any cardinal
  • \(\kappa\) typically a regular cardinal
  • \(K\) a small simplicial set (for some inaccessible cardinal)
  • \(X\) any simplicial set
  • \(p: K \rightarrow \mathcal{C}\) some infinity functor
  • \(\mathcal{C}, \mathcal{D}\) infinity categories
  • \(\mu\)-blabla: omitting the \(\mu\) typically means, that it holds for some cardinal \(\mu\) (in our fixed Universe)
  • \(\kappa\)-blablabla for a regular cardinal \(\kappa\): omitting the \(\kappa\) typically means \(\omega\)-blablabla (where \(\omega = \vert \mathbb{N} \vert\)
  • We won't jump universes in anything I have prepared.

sources

Content of my talk

Plan

  1. Motivation
  2. some set theory
  3. introduce "smallness" notions & filteredness
  4. introduce accessible & presentable categories
  5. alternative characterization of Acc/Pres. Categories using Ind
  6. Given time: \(\mathrm{An}\) and \(\mathrm{Cat}_{\infty}\) are presentable

motivation - necessity of set theory

Date: nil

Author: Anton Zakrewski

Created: 2024-12-19 Do 21:51