[Turkmath:6961] FGC-Higher Structures Seminars::Simona Paoli::21 January, 2025 at 18:00 Istanbul time

[kazimilhan.ikeda]

Sayın Matematikçiler,

21 Ocak 2025 Salı günü saat 18:00'da yapılacak Feza Gürsey Fizik ve 
Matematik UygAr Merkezi Yüksek Yapılar Seminerlerinde bu kez Simona 
Paoli (Univ. Aberdeen) konuşacaktır. Detaylar aşağıda yer almaktadır.

İyi çalışmalar,
İlhan İkeda

-------- Original Message --------

Dear friends,

On the 21st of January 2025 Tuesday at 18:00 Istanbul local time (15:00 
Aberdeen-UK local time),  Simona Paoli from the University of Aberdeen 
will be the speaker of Feza Gursey Center for Physics and Mathematics 
Higher Structures Research Group Seminars.

The details of Simona's seminar talk are as follows:

Speaker: Simona Paoli (University of Aberdeen, UK)

Date: January 21, 2025, Tuesday.

Time: 18:00 Istanbul local time (15:00 Aberdeen-UK local time)

Title: The weakly globular approach to higher categories

Abstract: Higher categories are motivated by naturally occurring 
examples in diverse areas of mathematics, including homotopy theory, 
mathematical physics, logic and computer sciences. Several different 
approaches exist to formalize the notion of a higher category. In this 
talk I will give an overview of an approach to model 'truncated' higher 
categories: namely those having higher morphisms in dimensions 0 up to n 
only. These arise naturally in homotopy theory, in modelling the 
building blocks of topological spaces, called n-types.

Classically, in a higher category we have sets of objects and sets of 
higher morphisms. This is also called 'globularity condition' as it is 
the condition that gives rise to the globular shape of the higher 
morphisms in a higher category. Instead, in the so called weakly 
globular approach I have introduced, the objects and the higher morphism 
do not form a set but a structure only equivalent (in a higher 
dimensional sense) to a set. We call this 'weak globularity condition'.

One advantage of this approach is that it is possible to model a weak 
n-category using a rather rigid structure, namely an n-fold category 
satisfying additional conditions. These are the weakly globular n-fold 
categories. I will mention some applications of these structures to 
homological algebra, as well as a link between weak globularity and the 
notion of weak units in the case n=2. I will conclude with some 
conjectures for general dimension n.

Given the highly technical nature of this work, and in the interest of 
making the talk broadly accessible, I will concentrate on the main ideas 
and intuitions, but more details can be found in the references below:

About weakly globular n-fold categories:

·       S. Paoli, Simplicial Methods for Higher Categories: Segal-type 
Models of Weak n-Categories, Algebra and Applications 26, Springer 
(2019).

·       S. Paoli, D. Pronk, A double categorical model of weak 
2-categories, _Theory and Application of categories_, 28, (2013), 
933-980.

About weak globularity and weak units:

·       S. Paoli, Weakly globular double categories and weak units, 
arXiv:2008.11180 (2024).

An application of weakly globular n-fold categories to homological 
algebra:

·       D. Blanc, S. Paoli, A model for the Andre-Quillen cohomology of 
an (\infty,1)-category, arXiv:2405.12674 (2024).

Zoom uygulaması Bilim Akademisi tarafından sağlanmaktadır./Zoom link is 
provided by The Science Academy.

Zoom link details:
(As usual the Zoom link will be active 30 minutes before the seminar 
time; that is at 17:30 Istanbul time/14:30 Aberdeen local time.)

Topic: FGC-Higher Structures Seminars

Date and time: Jan. 21, 2025 active for the period 17:30-20:30 Istanbul 
local time

Join Zoom Meeting
https://us02web.zoom.us/j/83013207597?pwd=DyOTGZeKvx8ayPtieqLF2AtMnu1muy.1

Meeting ID: 830 1320 7597
Passcode: 389958

Best regards,
Ilhan

Organized by Feza Gürsey Center for Physics and Mathematics
Supported by Bilim Akademisi - The Science Academy
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