[Turkmath:6123] FGC-Higher Structures Seminars::Atabey KAYGUN [May 23, 2023 at 17:00-Istanbul time]

[kazimilhan.ikeda]

Dear friends,

This coming week, on Tuesday, May 23, 2023 at 17:00 (Istanbul local 
time) our speaker for FGC-Higher Structures
Research Group Seminars is Atabey Kaygun from Istanbul Technical 
University.

The details of the seminar talk are as follows:

Speaker: Atabey Kaygun (Istanbul Technical University)
Date: May 23, 2023, Tuesday.
Time: 17:00 Istanbul local time.
Title: Dold-Kan equivalence and its extensions.
Abstract:
The Dold-Kan Correspondence is an equivalence between the category of 
differential graded objects and the
category of simplicial objects on an abelian category. This equivalence 
is best understood within the context
of Quillen model categories. However, a more straightforward 
interpretation using the representation theory
of small categories is possible. We will demonstrate that the Dold-Kan 
equivalence can be expressed through
specific induction and restriction functors, paving the way for similar 
equivalences for crossed-simplicial
objects. There are extensions to the Dold-Kan Correspondence in this 
context, with the Dwyer-Kan equivalence
between the category of duplicial objects and the category of cyclic 
objects over an abelian category being a
notable example. We will also show that the Dwyer-Kan equivalence can be 
incorporated into the framework we
initially developed for the Dold-Kan Correspondence. Lastly, we will 
discuss further extensions.
This research is a joint work with my PhD student, Haydar Can Kaya.

Zoom link details:
Please join Zoom Meeting, which will be active on Tuesday, May 23, 2023 
at 16:45 (Istanbul local time):

https://ozyegin-edu-tr.zoom.us/j/96956596842?pwd=cDNHQy8vR0lkMk8velhGZDdzU1p1UT09

Meeting ID: 969 5659 6842
Passcode: 442777

Best Regards,
K. Ilhan Ikeda
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