[Turkmath:7039] FGC-Higher Structures Seminars::Juan Orendain::06 March THURSDAY, 2025 at 18:00 Istanbul time

[kazimilhan.ikeda]

Sayın Matematikçiler,

Aşağıda FGC-Yüksek Yapılar Seminerleri kapsamında yapılacak konuşmanın 
detaylarını bulacaksınız. Salı günleri yapılan bu etkinlikleri, bir 
kereye mahsus olarak bu kez Perşembe günü yapacağımızı dikkatinize 
sunarım.

İyi çalışmalar,
ilhan ikeda

Dear friends,

On the 6th of March 2025 THURSDAY (note the unusual day!) at 18:00 
Istanbul local time (10:00 Cleveland local time),  Juan Orendain from 
Case Western Reserve University will be the speaker of the first talk of 
the Spring Semester of Feza Gursey Center for Physics and Mathematics 
Higher Structures Research Group Seminars.

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

Speaker: Juan Orendain (Case Western Reserve University)

Date: March 06, 2025, Thursday (note the unusual day!).

Time: 18:00 Istanbul local time (10:00 Cleveland local time)

Title: _Crossed products of decorated bicategories and length of 
__equipments_

Abstract_:_
Equipments are categorical structures of dimension 2 having two separate 
types of 1-arrows -vertical and horizontal- and supporting restriction 
and extension of horizontal arrows along vertical ones. Equipments are 
2-functors satisfying certain conditions, but they can also be 
understood as double categories satisfying a fibrancy condition. In the 
zoo of 2-dimensional categorical structures, they fit nicely between 
2-categories and double categories, and are generally considered as the 
2-dimensional categorical structures where synthetic category theory is 
done, and in reasonable cases, where monoidal bicategories are more 
naturally defined.

In this talk I discuss the problem of lifting a 2-category into an 
equipment along a given category of vertical arrows, and how this 
problem allows us to define a notion of length on general double 
categories. The length of a double category is a number that roughly 
measures the amount of work one needs to do to reconstruct the double 
category from a bicategory along its set of vertical arrows. I will 
review the length of double categories, and I will discuss the crossed 
product of a decorated bicategory construction -a method for 
constructing different double categories from a given bicategory is 
presented-. One of the main ingredients of the construction are 
so-called canonical squares. I will show that in certain classes of 
equipments -fully faithful and absolutely dense- every square that can 
be canonical is indeed canonical. I will explain how from this, it can 
be concluded that fully faithful and absolutely dense equipments are of 
length 1, and so they can be 'easily' reconstructed from their 
horizontal bicategories.

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/09:30 Cleveland time.)

Topic: FGC - Higher Structures Seminars - Spring Term

Date and Time: 06 March 2025 active for the period 17:30-20:00 Istanbul 
time

Join Zoom link
https://us02web.zoom.us/j/89763545977?pwd=lYGC8MH3sT6HYT0NSKLvyDkB14K0H7.1

Meeting ID: 897 6354 5977
Passcode: 467808

Best regards,
Ilhan

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