Reminder ItaCa Fest 2022

[Ivan Di Liberti <diliberti.math@gmail.com>]

Dear all,

this is a quick reminder that the ItaCa Fest will resume this week! As in the previous editions, the Fest collects a wide range of topics and represents a large number of communities.

The first date of the ItaCa Fest will be April 20, 2022 at 3 pm (Italian time):

- A. Lorenzin, Inner automorphisms as 2-cells.
- M. Karvonen, Formality and strongly unique enhancements.

The zoom link is the following: https://stockholmuniversity.zoom.us/j/68792232558
While the Fest website is this one: https://progetto-itaca.github.io/pages/fest22.html

A complete list of the speakers of this edition of the Fest: Coraglia, Kock, Bonchi, Blechschmidt, Cigoli, Reggio, Escardó, Capucci, Di Vittorio, Raptis.


Join us (and bring a friend)!

Cheers,
Beppe, Ivan, Edoardo, Fosco, Paolo.

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Karvonen.
Title: Inner automorphisms as 2-cells
Abstract: Thinking of groups as one-object categories makes the category of groups naturally into a 2-category. We observe that a similar construction works for any category: a 2-cell f->g is given by an inner automorphism of the codomain that takes f to g, where inner automomorphisms are defined in general using isotropy groups. We will explore the behavior of limits and colimits in the resulting 2-category: when the underlying category is cocomplete, the resulting 2-category has coequalizers iff the isotropy functor is representable - in the case of groups, this amounts to deducing the existence of HNN-extensions from the representability of id:Grp->Grp. Under reasonable conditions, limits and connected colimits in the underlying category are 2-categorical limits/colimits in the resulting 2-category. However, many other 2-dimensional limits and colimits fail to exist, unless the underlying category has only trivial inner automorphisms.

Lorenzin.
Title: Formality and strongly unique enhancements
Abstract: Inspired by the intrinsic formality of graded algebras, we give a characterization of strongly unique DG-enhancements for a large class of algebraic triangulated categories, linear over a commutative ring. We will discuss applications to bounded derived categories and bounded homotopy categories of complexes. For the sake of an example, the bounded derived category of finitely generated abelian groups has a strongly unique enhancement.



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