Table of contents
About this book
Introduction
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems.
In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results.
The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual form of modules over the Schur algebra.
Roman Mikhailov’s lectures highlight topological invariants:
homotopy and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology.Lastly, Antoine Touzé’s introductory course on homological algebra makes the book accessible to graduate students new to the field.
The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.
Keywords
Editors and affiliations
Bibliographic information
 Book Title Lectures on Functor Homology

Editors
Vincent Franjou
Antoine Touzé
 Series Title Progress in Mathematics
 Series Abbreviated Title Progress in Mathematics(Birkhäuser)
 DOI https://doi.org/10.1007/9783319213057
 Copyright Information Springer International Publishing Switzerland 2015
 Publisher Name Birkhäuser, Cham
 eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
 Hardcover ISBN 9783319213040
 Softcover ISBN 9783319793337
 eBook ISBN 9783319213057
 Series ISSN 07431643
 Series EISSN 2296505X
 Edition Number 1
 Number of Pages VI, 149
 Number of Illustrations 139 b/w illustrations, 1 illustrations in colour

Topics
Category Theory, Homological Algebra
Group Theory and Generalizations
Algebraic Topology
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