BIMSA > BIMSA Topology Seminar On the Non-Existence of Functors
On the Non-Existence of Functors
Organizers
Matthew Burfitt , Jing Yan Li , Jie Wu , Nanjun Yang , Jia Wei Zhou
Speaker
Sergei Ivanov
Time
Thursday, December 26, 2024 2:00 PM - 4:00 PM
Venue
A3-2a-302
Online
Zoom 482 240 1589 (BIMSA)
Abstract
Abstract: We consider several types of non-existence theorems for functors. For example, there are no nontrivial functors from the category of groups (or the category of pointed sets, or vector spaces) to any small category. Another type of questions that we consider are questions about nonexistence of subfunctors and quotients of the identity functor on the category of groups (or abelian groups). For example, there is no a natural non-trivial way to define an abelian subgroup of a group, or a perfect quotient group of a group. As an auxiliary result we prove that, for any non-trivial subfunctor Fof the identity functor on the category of groups, any group can be embedded into a simple group that lies in the essential image of F.
Speaker Intro
Prof. Sergei Ivanov is a mathematician from St. Petersburg, Russia. His research interests include homological algebra, algebraic topology, group theory, simplicial homotopy theory, simplicial groups.