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Online algebra seminar - 16th of September, 1pm PDF Print

We will continue online on Thursday, 16th of September, at 13.00 CEST on ZOOM platform and M5 lecture room (for information how to acces seminar and next programme visit this page) by the talk:

Nicholas Meadows

Higher theories and monads

Abstract:
We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories, and exploit this to prove many classical theorems about monads in the $\infty$-categorical setting. Amongst other things, we prove that the category of algebras for an accessible monad on a locally presentable $\infty$ category is locally presentable. We also apply the result to construct examples of $\infty$-categorical monads from pretheories.

Last Updated on Wednesday, 15 September 2021 15:40
 
Online algebra seminar - 19th of August, 1pm PDF Print

We will continue online on Thursday, 19th of August, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Charles Walker

The nerve of a relative monad

Abstract:
In this talk we will consider an embedding of monads into double categories, which sends a monad P to its (concrete) double category of P-embeddings (also called P split monos), as well as generalizations of this embedding the setting of (well-behaved) relative monads. By considering a more general notion of monad morphism (motivated by the relative setting), we will understand this embedding as a fully faithful nerve which exhibits the terminal monad as 'dense' with respect to these more general morphisms.

We will then give two applications of this construction. Firstly, we will give another approach by which one arrives at the “decagon type” axioms of last time, and secondly we will give a simpler proof of the reduced form of pseudo-distributive laws involving lax-idempotent pseudomonads. Note that some parts are a work in progress.

Last Updated on Monday, 16 August 2021 15:01
 
32nd mathematical hike - 31st of July 2021 PDF Print

Dear Friends of Hikes and Mathematics,

Extreme hike! The 32nd mathematical hike is planned on the 31st of July. Meet at 06:00 at the Main Train Station of Brno.

We go by train (leaves at 06:12), then approx. 53 km to get back to Brno. This means that there is no train to catch, no time pressure as at the 31st hike. This hike favours shorter options: you can leave at 19 and 36 km mark comfortably. Evaluate your strength and join us.

All information and photos can be found at https://conference.math.muni.cz/vylety/. (in CZ)

Have a nice summer, we look forward to you joining us.

Jana Bartoňová and Jonatan Kolegar, organizers
Jan Slovák, Director of the Department of Mathematics and Statistics

Last Updated on Friday, 16 July 2021 11:41
 
Online algebra seminar - June 24th, 1pm PDF Print

We will continue online on Thursday, June 24th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Giulio Lo Monaco

Vopěnka's principle in infinity-categories

Abstract:
Vopěnka's principle has arisen as a model theoretical statement, provably independent of ZFC set theory. However, there are a number of categorical ways of formulating it, preventing the existence of proper classes of objects with some conditions in presentable categories, and these are what our attention will be focused on. In particular, we will look at analogous statements in the context of oo-categories and we will ask how these new statements interact with the older ones. Moreover, some of the consequences of Vopěnka's principle on classes of subcategories of presentable categories are investigated and to some extent generalized to oo-categories. A parallel discussion is undertaken about the similar but weaker statement known as weak Vopěnka's principle.

Last Updated on Tuesday, 22 June 2021 15:36
 
Record of Department Assembly, June 16. at 4pm PDF Print

Recording available HERE

This year, the first regular Department Assembly will take place on Wednesday, June 16, at 4pm in the so called "hybrid" form. Thus, the real meeting in M1 will be streamed in real time, too, see the ZOOM meeting invitation below.

The online meeting will be chaired by doc. Jan Kolacek and the programme will involve my report on the department budgeting and development foresight, discussion and the item "other". After the Assembly, there will be a light refreshment served outside the building at the desks in front of the library (if the weather allows).

Last Updated on Thursday, 17 June 2021 15:02
 
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