Universität Augsburg

Herr Maximilian Kaske
Universität Augsburg
spricht am
Donnerstag, 24. September 2020
um
8:30 Uhr
im
Raum 2004 (L1)
über das Thema:
Abstract: 
André Joyal showed that a theory of higher categories can be developed by literally interpreting the language of category theory in the category of simplicial sets. Recent work by DenisCharles Cisinski expanded on this approach by giving a rather elementary construction of the universal left fibration  a morphism closely related to higher categorical counterpart of the category of sets. This once again raises questions of size and we take the opportunity to translate this construction to the lesserknown foundation ZFC/S. Observing that the commonly used axioms of universes can be replaced by the wellknown reflection principle of classical set theory, Solomon Feferman proposed ZFC/S as a possible solution to the sizue issues inherent to category theory. However, one now needs to consider "smalldefinability" and a stricter notion of "smallness" when working with categories and functors. Following the philosophy of Joyal and Cisinski, we show that these concepts have an interpretation in the higher categorical context as well and provide a construction of the universal left fibration in the sense of Feferman. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Marc NieperWißkirchen 