Institut für Mathematik Universität Heidelberg |

Homotopical Category Theory

Seminar by Lukas Waas and Christian Dahlhausen in winter term 2023/24.

Wednesday, 16:15--17:45 Uhr, Seminarraum 3 at Mathematikon (INF 205)

Content

In this seminar we will have a first glimpse into Homotopical Category Theory (a.k.a. Higher Category Theory) theory and we want to understand why oo-categories are useful and how to transfer concepts from ordinary category theory to homotopical category theory. We will not be able to spell out every technical detail, but rather focus on the main concepts and the ideas behind them.Here is programme of the seminar.

Talks

No. | Date | Title | Speaker |

1 | 18.10. | Introduction I | Dahlhausen |

2 | 25.10. | Introduction II | Waas |

3 | 08.11. | From 1-categories to oo-categories (and back) | Witt |

4 | 15.11. | From simplicial categories to quasi-categories | Klevesath |

5 | 22.11. | Anodyne maps and fibrations | Scholz |

6 | 29.11. | Mapping spaces, joins, and slices | Zahlen |

7 | 13.12. | Joyal's theorem: on invertible arrows | Dahlhausen |

8 | 10.01. | Fully faithfullness and essential surjectivity. | Scholz |

9 | 17.01. | Localisations of oo-categories, mapping spaces, fat joins, and fat slices | Waas |

10 | 24.01. | (Co)cartesian fibrations | Heger |

11 | 31.01. | Straightening-Unstraightening I | Heger |

12 | 07.01. | Straightening-Unstraightening II | Heger |

13 | 14.02. | The Yoneda-Lemma | Dahlhausen |

Organisatorial remarks

- This seminar is targeted at highly motivated and dedicated students who enjoy abstract structures.
- Participants should have basic knowledge about category theory and either topological homotopy theory or homological algebra.
- We expect every participant to be familiar with the content of section 1.1. in Land's book in the beginning of the seminar.
- If you are interested in participating in the seminar, please register at MÜSLI
*and*write an email to Christian Dahlhausen indicating your relevant background for the seminar.