Holdings: Lectures on functor homology

Lectures on functor homology:

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Bibliographic Details
Other Authors:	Franjou, Vincent 1959- (Editor), Touzé, Antoine (Editor)
Format:	Electronic eBook
Language:	English French
Published:	Cham Birkhäuser [2015] Cham Springer
Series:	Progress in mathematics volume 311
Subjects:	Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik
Online Access:	BTU01 TUM01 UBM01 UBT01 UBW01 UEI01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource (vi, 149 Seiten) Illustrationen
ISBN:	9783319213057 9783319213040
DOI:	10.1007/978-3-319-21305-7

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Record in the Search Index

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adam_text	LECTURES ON FUNCTOR HOMOLOGY / : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS INTRODUCTION A. DJAMENT: HOMOLOGIE STABLE DES GROUPES A COEFFICIENTS POLYNOMIAUX W. VAN DER KALLEN:LECTURES ON BIFUNCTORS ANDFINITE GENERATION OF RATIONALCOHOMOLOGY ALGEBRAS R. MIKHAILOV: POLYNOMIAL FUNCTORS AND HOMOTOPY THEORY A. TOUZE: PREREQUISITES OF HOMOLOGICAL ALGEBRA DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. LECTURES ON FUNCTOR HOMOLOGY / : 2015 ABSTRACT / INHALTSTEXT 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 AURELIEN 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 THE SERIES INCLUDES AN INTRIGUING DEVELOPMENT OF SCORICHENKO’S UNPUBLISHED RESULTS.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 TOUZE’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 DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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spelling	Lectures on functor homology Vincent Franjou, Antoine Touzé, editors Cham Birkhäuser [2015] Cham Springer 1 Online-Ressource (vi, 149 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Progress in mathematics volume 311 Beiträge in englischer und französischer Sprache Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik Franjou, Vincent 1959- (DE-588)114366357 edt Touzé, Antoine (DE-588)1081398353 edt Progress in mathematics volume 311 (DE-604)BV035421267 311 https://doi.org/10.1007/978-3-319-21305-7 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730341&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730341&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Lectures on functor homology Progress in mathematics Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik
title	Lectures on functor homology
title_auth	Lectures on functor homology
title_exact_search	Lectures on functor homology
title_full	Lectures on functor homology Vincent Franjou, Antoine Touzé, editors
title_fullStr	Lectures on functor homology Vincent Franjou, Antoine Touzé, editors
title_full_unstemmed	Lectures on functor homology Vincent Franjou, Antoine Touzé, editors
title_short	Lectures on functor homology
title_sort	lectures on functor homology
topic	Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik
topic_facet	Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik
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volume_link	(DE-604)BV035421267
work_keys_str_mv	AT franjouvincent lecturesonfunctorhomology AT touzeantoine lecturesonfunctorhomology

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