Další seminář z algebry se koná 30.10.2019 od 13.00 v zasedací místnosti ve druhém patře.

E. Lanari

Cartesian fibrations of (oo,2)-categories

Abstrakt:
The problem of dealing with infinitely many coherence constraints in oo-category theory when trying to define oo-functors has lead to a fibrational approach, in which one represents diagrams of the form B-->Cat_oo as a suitable kinds of fibrations over B. While this is a theorem, due to Lurie, in the case of oo-categories (i.e. (oo,1)-categories), so far there has been no combinatorial definition of a cartesian fibration of (oo,2)-categories.

In this talk, I will define cartesian fibrations in this context, prove some of their basic properties and show they are equivalent (under a suitable equivalence of (oo,2)-categories) to the counterpart in the context of categories enriched over marked simplicial sets (where the definition is given, mutatis mutandis, based on what happens with 2-categories). Furthermore, I will prove some statements made by Gaitsgory and Rozemblyum concerning locally cartesian fibrations and (oo,2)-categories fibred over (oo,1)-categories, thus substantiating the validity of our definition.

Další seminář z algebry se koná 24.10.2019 od 13.00 v posluchárně M5.

R. Stenzel

From Univalence to descent via "split indexed quasi-categories", part 2

Abstrakt:
In the last talk I sketched the definitions of univalent fibrations, complete Segal spaces and Grothendieck infinity-toposes.
On Thursday we will continue where we left off and relate these notions to one another, and, in that light, revisit the weak equivalence extension property and the fibration extension property of model categories.