Derived functors of non-additive functors
In this course we are studying various topics in the simplicial homotopy theory. This semester we will discuss the theory of derived functors of non-additive functors. After a brief reminder of a classical theory of derived functors, we will follow the seminal paper of Dold and Puppe on the topic. Relation to homology of symmetric powers and Eilenberg-Maclane spaces will be discussed as well. If time permits, we will also look at the general theory of derived functors in an abstract homotopy-theoretical context.
Lecturer
Fedor Pavutnitskiy
Date
27th September ~ 20th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 10:40 - 15:05 | A3-3-201 | ZOOM 09 | 230 432 7880 | BIMSA |
Prerequisite
category theory, homological algebra, homotopy theory
Syllabus
1. Derived functors in homological algebra
2. Derived functors in simplicial homotopy theory
3. Dold-Kan correspondence, generalized Eilenberg-Zilber theorem
4. Applications of suspension homomorphism and bar construction
2. Derived functors in simplicial homotopy theory
3. Dold-Kan correspondence, generalized Eilenberg-Zilber theorem
4. Applications of suspension homomorphism and bar construction
Reference
Dold, A., & Puppe, D. (1961). Homologie nicht-additiver funktoren. anwendungen. In Annales de l'institut Fourier (Vol. 11, pp. 201-312).
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
I'm working in simplicial homotopy theory and its applications in path homology and homological algebra related to groups and Lie algebras. I'm also interested in applications of deep learning in contemporary mathematics.