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

Jiří Adámek

C-Varieties of Ordered and Quantitative Algebras

Abstract:
Mardare, Panangaden and Plotkin introduced c-varieties of algebras on metric spaces. These are categories of metric-enriched algebras specified by equations in a context. A context puts restrictions on the distances of variables one uses. We prove that c-varieties are precisely the monadic categories over Met for countably accessible enriched monads preserving epimorphisms.

We analogously introduce c-varieties of ordered algebras as categories specified by inequalities in a context. Which means that conditions on inequalities between variables are imposed. We prove that c-varieties precisely correspond to enriched finitary monads on Pos preserving epimorphisms.

This is joint work with Jiri Rosicky.

We will continue online on Thursday, March 25th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Jonathan Kirby

A model-theoretic look at exponential fields

Abstract:
An exponential function is a homomorphism from the additive group of a field to its multiplicative group. The most important examples are the real and complex exponentials, and these are naturally studied analytically.
However, one can also study the algebra of exponential fields and their logical theory. It turns out that the natural ways to do this take one outside the usual finitary classical logic of model theory and into positive/coherent logic, geometric logic, or other infinitary logics, or to the more algebraic and abstract setting of accessible categories.

I will describe some of this story, focussing on the more algebraic aspects of existentially closed exponential fields.

This is joint work with Levon Haykazyan.

We will continue online on Thursday, March 18th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Karol Szumilo

Infinity groupoids in lextensive categories

Abstract:
I will discuss a construction of a new model structure on simplicial objects in a countably lextensive category (i.e., a category with well behaved finite limits and countable coproducts). This builds on previous work on a constructive model structure on simplicial sets, originally motivated by modelling Homotopy Type Theory, but now applicable in a much wider context. This is joint work with Nicola Gambino, Simon Henry and Christian Sattler.

Dear colleagues,

the magazine obituary about Libor Polák will be published in the journal Semigroup Forum.

It is available at:

https://link.springer.com/article/10.1007/s00233-021-10177-y