# Abstracts for Conference for Young researchers in homotopy theory and categorical structures, February 13-15, 2017

Alternatively have a look at the program.

## Homotopical Morita theory for corings

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Speaker:
Kathryn Hess
Affiliation:
EPF Lausanne
Date:
Mon, 2017-02-13 09:30 - 10:30
Location:
MPIM Lecture Hall

(Joint work with Alexander Berglund)

## Galois extensions in motivic homotopy theory

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Speaker:
Magdalena Kedziorek
Affiliation:
EPF Lausanne
Date:
Mon, 2017-02-13 11:00 - 11:30
Location:
MPIM Lecture Hall

Galois extensions of ring spectra in classical homotopy theory were introduced by Rognes.
In this talk I will discuss a general formal framework to study homotopical Galois extensions and
concentrate on the applications to motivic homotopy theory. I will discuss several examples of
homotopical Galois extensions in motivic setting comparing them to the ones known from classical
homotopy theory.

This is a joint project with Agnès Beaudry, Kathryn Hess, Mona Merling and Vesna Stojanoska.

## Higher enveloping algebras and configuration spaces of manifolds

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Speaker:
Benjamin Knudsen
Affiliation:
Harvard University
Date:
Mon, 2017-02-13 11:45 - 12:15
Location:
MPIM Lecture Hall

I will describe a construction providing Lie algebras with enveloping algebras over the operad of little $n$-dimensional
disks for any $n$. These algebras enjoy a combination of good formal properties and computability, the latter afforded
by a Poincaré-Birkhoff-Witt type result. The main application pairs this theory with the theory of factorization homology
in a study of the rational homology of configuration spaces, leading to a wealth of computations, improvements of classical results, and a combinatorial proof of homological stability.

## The structure of the category of strickt n-categories

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Speaker:
Dimitri Ara
Affiliation:
Aix-Marseille Université
Date:
Mon, 2017-02-13 14:00 - 15:00
Location:
MPIM Lecture Hall

The category n-Cat of strict n-categories and strict n-functors is endowed with
a rich structure that is only partially understood. First, it is endowed with a tensor
product, generalizing Gray's tensor product of 2-categories, first defined by Al-Alg
and Steiner in the early 90's. This implies that n-Cat, endowed with lax transformations
and higher lax transformations, form an n-Gray-category in some appropriate sense.
Second, it is endowed with a join construction, generalizing the join construction of

## Cubical $(\omega,p)$-categories

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Speaker:
Maxime Lucas
Affiliation:
Université Paris 7
Date:
Mon, 2017-02-13 15:15 - 15:45
Location:
MPIM Lecture Hall

Handling higher structures such as higher categories usually involves conceiving them as conglomerates of
cells of certain shape. Such shapes include simplices, globes, or cubes. The aim of this talk is to bridge the
gap between two such results:

The first one is the equivalence between cubical and globular $\omega$-groupoids. Although this equivalence
is useful in theory, in practice it is complicated to make explicit the functors composing this equivalence. This

## Gong Show, I (Conference for Young researchers in homotopy theory and categorical structures)

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Date:
Mon, 2017-02-13 16:45 - 17:45

Speakers, titles and abstracts, see this PDF.

## Clone of Gong Show, II (Conference for Young researchers in homotopy theory and categorical structures)

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Date:
Mon, 2017-02-13 19:30 - 20:30
Location:
MPIM Lecture Hall

Speakers, titles and abstracts, see this PDF.

## Open discussion (Conference for Young researchers in homotopy theory and categorical structures)

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Date:
Mon, 2017-02-13 20:30 - 21:30
Location:
MPIM Lecture Hall

## 2-Segal sets and the Waldhausen construction

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Speaker:
Martina Rovelli
Affiliation:
EPF Lausanne
Date:
Tue, 2017-02-14 09:30 - 10:30
Location:
MPIM Lecture Hall

$2$-Segal objects, which are a generalisation of ordinary Segal objects, were introduced and studied by
Dyckerhoff-Kapranov and Gálvez-Kock-Tonks. An important example of a $2$-Segal object is the Waldhausen
construction of an exact category. The Waldhausen construction makes sense for a more general input, and the
goal of the talk is to explain that, in the discrete setting, the Waldhausen construction is in fact quite exhaustive.
More precisely, it induces an equivalence between the category of stable pointed double categories and the

## On the category of Poisson Hopf algebras

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Speaker:
Ana Agore
Affiliation:
Vrije Universiteit Brussel
Date:
Tue, 2017-02-14 11:00 - 11:30
Location:
MPIM Lecture Hall

A Poisson Hopf algebra is both a Poisson algebra and a Hopf algebra such that the comultiplication and
the counit are morphisms of Poisson algebras. Such objects are situated at the border between Poisson
geometry and quantum groups.  We investigate the category of Poisson Hopf algebras with respect to
properties such as (co)completeness or existence of (co)free objects. For instance, we prove that there
exists a free Poisson Hopf algebra on any coalgebra or, equivalently that the forgetful functor from the

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