Online algebra seminar  April 15th, 1pm 


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 firstorder theories we classify theories using combinatorial properties. The most wellknown class is that of stable theories, which are very wellbehaved. 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 stablelike independence relations in accessible categories. Inspired by this we introduce the framework of AECats (abstract elementary categories) and prove canonicity for simplelike and NSOP_1like independence relations. This way we reconstruct part of the hierarchy that we have for firstorder theories, but now in the very general categorytheoretic setting. 
Last Updated on Tuesday, 13 April 2021 08:34 

Online algebra seminar  April 8th, 1pm 


We will continue online on Thursday, April 8th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Michael Ching
Tangent ∞categories and Goodwillie calculus
Abstract: In 1984 Rosický introduced tangent categories in order to capture axiomatically some properties of the tangent bundle functor on the category of smooth manifolds and smooth maps. Starting in 2014 Cockett and Cruttwell have developed this theory in more detail to emphasize connections with cartesian differential categories and other contexts arising from computer science and logic. In this talk I will discuss joint work with Kristine Bauer and Matthew Burke which extends the notion of tangent category to ∞categories. To make this generalization we use a characterization by Leung of tangent categories as modules over a symmetric monoidal category of Weilalgebras and algebra homomorphisms. Our main example of a tangent ∞category is based on Lurie's model for the tangent bundle to an ∞category itself. Thus we show that there is a tangent structure on the ∞category of (differentiable) ∞categories. This tangent structure encodes all the higher derivative information in Goodwillie's calculus of functors, and sets the scene for further applications of ideas from differential geometry to higher category theory. 
Last Updated on Monday, 05 April 2021 20:14 
Online algebra seminar  April 1st, 1pm 


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
CVarieties of Ordered and Quantitative Algebras
Abstract: Mardare, Panangaden and Plotkin introduced cvarieties of algebras on metric spaces. These are categories of metricenriched algebras specified by equations in a context. A context puts restrictions on the distances of variables one uses. We prove that cvarieties are precisely the monadic categories over Met for countably accessible enriched monads preserving epimorphisms. We analogously introduce cvarieties of ordered algebras as categories specified by inequalities in a context. Which means that conditions on inequalities between variables are imposed. We prove that cvarieties precisely correspond to enriched finitary monads on Pos preserving epimorphisms. This is joint work with Jiri Rosicky. 
Last Updated on Thursday, 01 April 2021 09:42 
Online algebra seminar  March 25th, 1pm 


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 modeltheoretic 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. 
Last Updated on Wednesday, 24 March 2021 07:58 
Online algebra seminar  March 18th, 1pm 


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. 
Last Updated on Monday, 15 March 2021 15:16 

