Lectures SS 2025

Speaker: Tessa Kammermeier, Universität Hamburg – Invited by Catherine Meusburger

Abstract: The notion of idempotent morphisms admitting splittings is important in algebraic theories such as K-theory, topological quantum field theories and many more. This is because the existence of idempotent splittings corresponds to the existence of a class of colimits that is, in some sense, minimal. These colimits, which are preserved by all functors, are called absolute. In categories where not all idempotents split, we would like take a completion to add only these absolute colimits. This is called the Karoubi or Cauchy completion of a category.

In this talk, I will sketch the proof of why idempotent splittings correspond to absolute colimits and outline the construction of the Karoubi and the Cauchy completion of a category, which will turn out to be equivalent. Furthermore, I will talk about a 2-categorical analogue of the Karoubi completion and, if time permits, talk about how this corresponds to a higher form of absolute colimits.

Speaker: Ivan Penkov, Constructor University Bremen – Invited by Karl-Hermann Neeb

Speaker: Mikael Rørdam, University of Copenhagen – Invited by Kang Li