LEADER 04755nam 22006975 450 001 9910300255003321 005 20200705053507.0 010 $a3-319-21305-9 024 7 $a10.1007/978-3-319-21305-7 035 $a(CKB)3710000000532418 035 $a(EBL)4188196 035 $a(SSID)ssj0001597321 035 $a(PQKBManifestationID)16297081 035 $a(PQKBTitleCode)TC0001597321 035 $a(PQKBWorkID)14885403 035 $a(PQKB)11036463 035 $a(DE-He213)978-3-319-21305-7 035 $a(MiAaPQ)EBC4188196 035 $a(PPN)190885610 035 $a(EXLCZ)993710000000532418 100 $a20151208d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Functor Homology$b[electronic resource] /$fedited by Vincent Franjou, Antoine Touzé 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (154 p.) 225 1 $aProgress in Mathematics,$x0743-1643 ;$v311 300 $aDescription based upon print version of record. 311 $a3-319-21304-0 320 $aIncludes bibliographical references. 327 $aIntroduction -- A. Djament: Homologie stable des groupes à coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touzé: Prerequisites of Homological Algebra. 330 $aThis book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament?s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko?s unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert?s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin?s strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov?s lectures highlight topological invariants: homotopy and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touzé?s introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems. 410 0$aProgress in Mathematics,$x0743-1643 ;$v311 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aGroup theory 606 $aAlgebraic topology 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aGroup theory. 615 0$aAlgebraic topology. 615 14$aCategory Theory, Homological Algebra. 615 24$aGroup Theory and Generalizations. 615 24$aAlgebraic Topology. 676 $a514.23 702 $aFranjou$b Vincent$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aTouzé$b Antoine$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300255003321 996 $aLectures on functor homology$91522731 997 $aUNINA