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Online algebra seminar - October 29th, 1pm PDF Print

We will continue online on Thursday, October 29th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Jiří Rosický

Injectivity in metric-enriched categories

Abstract:
Among Banach spaces approximate injectivity is more important than injectivity. We will treat it from the point of view of enriched category theory - as enriched injectivity over complete metric spaces.

Last Updated on Thursday, 29 October 2020 08:48
 
Online differential geometry seminar - October 26, 10am PDF Print

The seminar on differential geometry will continue with this lecture:

October 26, 10amonline on MS Teams

Join via this LINK.

Keegan Flood (our new researcher, Masaryk university):

The geometry of a certain class of singular solutions to the c-projective metrizability equation

Abstract:

A nondegenerate solution to the c-projective metrizability equation is equivalent to a quasi-Kahler metric that is compatible with the c-projective class. By replacing this nondegeneracy condition on a solution to the metrizability equation with a nondegeneracy condition on its prolonged system we get a curved orbit decomposition of the underlying manifold where the open orbits inherit quasi-Kahler metrics and the closed orbits inherit CR-structures of hypersurface type. We may also examine the analogue of these considerations in the setting of projective geometry.

Last Updated on Thursday, 22 October 2020 08:29
 
Online algebra seminar - October 22nd, 1pm PDF Print

We will continue online on Thursday, October 22nd, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Christian Espindola

Categoricity in infinite quantifier theories

Abstract:
Morley's categoricity theorem states that a countable first-order theory categorical in some uncountable cardinal is categorical in all uncountable cardinals. Shelah's categoricity conjecture states that a similar eventual categoricity behavior holds for certain infinitary theories in finite quantifier languages. In this talk we will explain the main ideas of a work in progress aiming at a version of eventual categoricity for theories in infinite quantifier languages. On the categorical side this corresponds to accessible categories, where the notion of internal size is taken instead of the cardinality of the underlying model. We will start motivating this with some examples computing the categoricity spectrum of infinite quantifier theories. Then we will study also to which extent the Generalized Continuum Hypothesis can be avoided through forcing techniques and how the use of large cardinals can replace model-theoretic assumptions like directed colimits or amalgamation. Our ultimate goal is to determine whether large cardinals are really needed for these latter assumptions or whether they just follow instead from categoricity.

Last Updated on Wednesday, 21 October 2020 08:41
 
Online algebra seminar - October 15th, 1pm PDF Print

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

Taichi Uemura

The universal exponentiable arrow

Abstract:
Cartmell showed that the category of generalized algebraic theories is equivalent to the category of contextual categories. This implies that the theory of generalized algebraic theories is essentially algebraic. We characterize the essentially algebraic theory of generalized algebraic theories as the free category with finite limits and with an exponentiable arrow.

The main theorem and a syntactic proof are found in arXiv:2001.09940. In this talk we give a semantic proof.

Last Updated on Wednesday, 14 October 2020 15:27
 
Online algebra seminar - October 8th, 1pm PDF Print

We will continue online on Thursday, October 8th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Christina Vasilakopoulou

Oplax Hopf Algebras

Abstract:
Hopf categories were introduced by Batista, Caenepeel and Vercruysse in 2016, as a many-object generalization of Hopf algebras linked to other notions like multiplier Hopf algebras and with applications to categorical Galois theory. What is of particular interest is that the multiplication and comultiplication appear to make use of different monoidal products: Gabriella Bohm in subsequent work expressed Hopf categories as specific opmonoidal monads. In our work, we follow a different direction of generalizing Hopf monoids in a braided monoidal bicategory, that allows us to realize Hopf categories as Hopf-type objects over the same monoidal product, restoring in a sense the self-dual feature of classical Hopf algebras. In this talk, we introduce oplax bimonoids and oplax Hopf monoids in an arbitrary braided monoidal bicategory, we study their main properties and we exemplify such structures in a Span-type bicategory where they return semi-Hopf and Hopf categories.

This is a report on joint work with Mitchell Buckley, Timmy Fieremans and Joost Vercruysse.

Last Updated on Wednesday, 07 October 2020 15:17
 
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