Lectures on Functor Homology
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The work Lectures on Functor Homology represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Lectures on Functor Homology
Resource Information
The work Lectures on Functor Homology represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Lectures on Functor Homology
 Statement of responsibility
 edited by Vincent Franjou, Antoine Touzé
 Subject

 Group Theory and Generalizations
 Algebraic topology
 Homological algebra
 Category theory (Mathematics)
 Group theory
 Algebraic Topology
 Electronic resources
 Category Theory, Homological Algebra
 Mathematics
 Algebraic Topology
 Homological algebra
 Algebraic topology
 Mathematics
 Group theory
 Category theory (Mathematics)
 Language
 eng
 Summary
 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 The series includes an intriguing development of Scorichenko’s unpublished results.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
 Image bit depth
 0
 LC call number
 QA169
 Literary form
 non fiction
 Series statement
 Progress in Mathematics,
 Series volume
 311
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