Itaca Fest 2024

ItaCa Fest is an online webinar aimed to gather the community of ItaCa.

The seminar will be live on Zoom at this link. The time is: 3pm Italian time.

Here the list of seminars

• April 10, 2024
• May 7, 2024
• June 5, 2024
• September 25, 2024
• October 22, 2024
• November 20, 2024

April 10, 2024

Pierre-Alain Jacqmin

Surjection-like classes of morphisms

Many classes of epimorphisms are considered in the literature with the aim of generalizing surjective functions from the category Set of sets to an arbitrary category. However, some of them fail to have specific desirable properties. In this talk, we are interested in classes of morphisms which interact with finite limits as surjections do in Set. More precisely, we study classes of morphisms in finitely complete categories which admit a "good" embedding in a presheaf category. By good embedding, we mean a functor which preserves and reflects finite limits and the classes of morphisms involved. We will examine both the conservative faithful and the fully faithful cases. Our main result is a complete characterization of those classes of morphisms via simple and well-known properties.

Manuel Mancini

On the representability of actions of non-associative algebras

It is well known that in the semi-abelian category Grp of groups, internal actions are represented by automorphisms. This means that the category Grp is action representable and the actor of a group X is the group Aut(X). The notion of action representable category has proven to be quite restrictive: for instance, if a non-abelian variety of non-associative algebras, over an infinite field of characteristic different from two, is action representable, then it is the category of Lie algebras. More recently G. Janelidze introduced the notion of weakly action representable category, which includes a wider class of categories.
In this talk we show that for an algebraically coherent variety of algebras and an object X of it, it is always possible to construct a partial algebra E(X), called external weak actor of X, which allows us to describe internal actions on X. Moreover, we show that the existence of a weak representation is connected to the amalgamation property and we give an application of the construction of the external weak actor in the context of varieties of unitary algebras.

Alan Cigoli

From Yoneda's additive regular spans to fibred cartesian monoidal opfibrations

It is well known that group cohomology can be interpreted in terms of equivalence classes of crossed extensions, the abelian group structure being given by the so-called Baer sums. By analogy, an intrinsic definition of cohomology in strongly semi-abelian categories, or more generally in exact Mal'tsev categories (Bourn-Rodelo), is given. In this talk, I will explain how Baer sums can be formally derived from the fibred/cofibred nature of the category of all crossed extensions of a given length. This point of view turns out to be very close to Yoneda's theory of Ext groups. We will see how his notion of additive regular span is actually an instance of fibred cartesian monoidal opfibration. Time permitting, I will give some hint on how this formal point of view can be carried on to a 2-dimensional level, thus giving a notion of cohomology 2-group.
(based on joint works with S. Mantovani, G. Metere and E.M. Vitale

May 7, 2024

Sebastian Wolf

TBA

TBA

Franco Rota

TBA

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Viktoriya Ozornova

TBA

TBA

June 5, 2024

Luigi Santocanale

TBA

TBA

Jonathan Weinberger

TBA

TBA

TBA

TBA

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September 25, 2024

Dario Stein

TBA

TBA

Danel Ahman

TBA

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Matthew Di Meglio

TBA

TBA

October 22, 2024

John Bourke

TBA

TBA

Giacomo Tendas

TBA

TBA

Luca Mesiti

TBA

TBA

November 20, 2024

Nicola Carissimi

TBA

TBA

TBA

TBA

TBA

TBA

TBA

TBA