Homological algebra : the interplay of homology with distributive lattices and orthodox semigroups
 Responsibility
 Marco Grandis.
 Language
 English.
 Imprint
 Singapore ; Hackensack, NJ : World Scientific, c2012.
 Physical description
 xi, 369 p. : ill. ; 24 cm.
Access
Available online
 www.worldscientific.com World Scientific
 ebrary
Math & Statistics Library

Stacks

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QA169 .G73 2012

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QA169 .G73 2012
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Creators/Contributors
 Author/Creator
 Grandis, Marco.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 357361) and index.
 Contents

 Introduction Coherence and Models in Homological Algebra PuppeExact Categories Involutive Categories Categories of Relations as RECategories Theories and Models Homological Theories and Their Universal Models Appendix A: Some Points of Category Theory Appendix B: A Proof for the Universal Exact System.
 (source: Nielsen Book Data)
 Publisher's Summary
 In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations. These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system. The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a 'Coherence Theorem for homological algebra'. (On the contrary, a 'nondistributive' homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.) The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences. We thus establish an effective method of working with spectral sequences, called 'crossword chasing', that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.
(source: Nielsen Book Data)
Subjects
 Subject
 Algebra, Homological.
Bibliographic information
 Publication date
 2012
 ISBN
 9789814407069
 9814407062