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)


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.


118.10.Introduction IDahlhausen
225.10.Introduction IIWaas
308.11.From 1-categories to oo-categories (and back)Witt
415.11.From simplicial categories to quasi-categoriesKlevesath
522.11.Anodyne maps and fibrationsScholz
629.11.Mapping spaces, joins, and slicesZahlen
713.12.Joyal's theorem: on invertible arrowsDahlhausen
810.01.Fully faithfullness and essential surjectivity.Scholz
917.01.Localisations of oo-categories, mapping spaces, fat joins, and fat slicesWaas
1024.01.(Co)cartesian fibrationsHeger
1131.01.Straightening-Unstraightening IHeger
1207.01.Straightening-Unstraightening IIHeger
1314.02.The Yoneda-LemmaDahlhausen

Organisatorial remarks

For any inquiries, please contact Christian Dahlhausen or Lukas Waas.