Homological Algebra: The Interplay Of Homology With Distributive Lattices And Or

Description: Homological Algebra: The Interplay Of Homology With Distributive Lattices And Orthodox Semigroups by Marco Grandis Explores various aspects of coherence in homological algebra that already appear in the classical situation of abelian groups or abelian categories. This title includes lattices of subobjects that are shown to play an important role in study of homological systems, from simple chain complexes to the structures that give rise to spectral sequences. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 non-distributive 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. Author Biography Marco Grandis is Professor in the Department of Mathematics at the University of Genoa, Italy. Table of Contents Introduction; Coherence and Models in Homological Algebra; Puppe-Exact Categories; Involutive Categories; Categories of Relations as RE-Categories; 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. Details ISBN9814407062 Author Marco Grandis Publisher World Scientific Publishing Co Pte Ltd ISBN-10 9814407062 ISBN-13 9789814407069 Format Hardcover Imprint World Scientific Publishing Co Pte Ltd Subtitle The Interplay of Homology with Distributive Lattices and Orthodox Semigroups Place of Publication Singapore Country of Publication Singapore DEWEY 512.55 Short Title HOMOLOGICAL ALGEBRA Language English Media Book Illustrations Yes Pages 384 Affiliation Univ Di Genova, Italy Year 2012 UK Release Date 2012-08-21 Publication Date 2012-08-21 Audience Postgraduate, Research & Scholarly We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:126695911;

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