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Homological Algebra: The Interplay Of Homology With Distributive Lattices And Or
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Item specifics
- Condition
- Book Title
- Homological Algebra: The Interplay Of Homology With Distributive
- ISBN
- 9789814407069
- Publication Year
- 2012
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Publication Name
- Homological Algebra: the Interplay of Homology with Distributive Lattices and Orthodox Semigroups
- Publisher
- World Industries Scientific Publishing Co Pte LTD
- Subject
- Mathematics
- Number of Pages
- 384 Pages
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Product Information
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.
Product Identifiers
Publisher
World Industries Scientific Publishing Co Pte LTD
ISBN-13
9789814407069
eBay Product ID (ePID)
116010293
Product Key Features
Publication Name
Homological Algebra: the Interplay of Homology with Distributive Lattices and Orthodox Semigroups
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
2012
Type
Textbook
Number of Pages
384 Pages
Additional Product Features
Country/Region of Manufacture
Singapore
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Orbiting Books
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