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.

Dear colleagues,
let me invite you to the habilitation lecture of John Bourke, PhD., which will be held on Tuesday, April 27, 2021, at 16 via Zoom

https://cesnet.zoom.us/j/92131900502?pwd=blduc1JWRGhobU5DSHJXVkNDWmxIdz09

Meeting ID: 921 3190 0502
Passcode: 510616

TITLE: Factorisation systems in algebra and homotopy theory.

Jiří Rosický
Chairman of the Habilitation Board

We will continue online on Thursday, April 15th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Mark Kamsma

Independence Relations in Abstract Elementary Categories

Abstract:
In Shelah's classification of first-order theories we classify theories using combinatorial properties. The most well-known class is that of stable theories, which are very well-behaved. Simple theories are more general, and then even more general are the NSOP_1 theories. We can characterise those classes by the existence of a certain independence relation. For example, in vector spaces such an independence relation comes from linear independence. Part of this characterisation is canonicity of the independence relation: there can be at most one nice enough independence relation in a theory.

Lieberman, Rosický and Vasey proved canonicity of stable-like independence relations in accessible categories. Inspired by this we introduce the framework of AECats (abstract elementary categories) and prove canonicity for simple-like and NSOP_1-like independence relations. This way we reconstruct part of the hierarchy that we have for first-order theories, but now in the very general category-theoretic setting.