We will continue online on Thursday, May 6th, the special time of 14.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Walter Tholen

Spaces vs Categories, Perfect Maps vs Discrete Cofibrations

Abstract:
We consider perfect maps of topological spaces and discrete cofibrations of categories to guide us into Burroni's notions of T-category and T-functor. In that environment we establish a so-called comprehensive factorization system that entails the classical Street-Walters system, as well as the (antiperfect, perfect)-system for continuous maps of Tychonoff spaces known since the 1960s.

(Based on joint work with Leila Yeganeh)

MASH AWARD for our department:

Stanislav Sobolevsky, Associate Professor at the New York University, has been awarded the Advanced MASH Belarus Award with his project DIGITAL CITY aimed at building the Digital City Engine and the Urban Network Artificial Intelligence at our department. The project will serve as seed funding for activities in the hot area of Smart Cities, as well as Network Science in general.

MASH AWARD for our department:

John Denis Bourke has been awarded the MASH Junior Award! Congratulation!

The Masaryk University Award in Sciences and Humanities has been extended  by the junior version. This year, John's award is the only one in the Physical Sciences section. The project will bring essential financial boost to John's research in the coming 3-5 years.

We will continue online on Thursday, April 29th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Hoang Kim Nguyen

Contravariant Homotopy Theories and Quillen’s Theorem A

Abstract:
In this talk I will show how to construct a model structure on a locally presentable category with a suitable cylinder object such that the model structure behaves in a ”covariant” or ”contravariant” way with respect to the cylinder. Examples of such model structures include the covariant and contravariant model structures on simplicial sets and the cocartesian and cartesian model structures on marked simplicial sets modelling presheaves with values in ∞-groupoids and ∞-categories respectively.

The model structures come with an abstract notion of cofinal functor which recovers the usual definition of cofinal functor for ∞-categories when applied to the covariant and contravariant model structures on simplicial sets. When applied to presheaves valued in n-types, one obtains a version of Quillen’s Theorem A for n-categories.