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Online seminář z algebry - 1.4.2021 PDF Tisk

Další seminář z algebry se koná 1.4.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Jiří Adámek

C-Varieties of Ordered and Quantitative Algebras

Abstrakt:
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.

Aktualizováno Čtvrtek, 01 Duben 2021 09:40
 
Online seminář z algebry - 25.3.2021 PDF Tisk

Další seminář z algebry se koná 25.3.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Jonathan Kirby

A model-theoretic look at exponential fields

Abstrakt:
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.


Aktualizováno Středa, 24 Březen 2021 07:56
 
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