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Homological algebra : = the interpla...

Grandis, Marco.

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Homological algebra : = the interplay of homology with distributive lattices and orthodox semigroups /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Homological algebra :/ Marco Grandis.
其他題名:	the interplay of homology with distributive lattices and orthodox semigroups /
作者:	Grandis, Marco.
出版者:	Singapore ;World Scientific, : c2012.,
面頁冊數:	xi, 369 p. :ill. ;24 cm.
標題:	Algebra, Homological. -
ISBN:	9789814407069 (hbk.) :

Homological algebra : = the interplay of homology with distributive lattices and orthodox semigroups /
Grandis, Marco.

Homological algebra :the interplay of homology with distributive lattices and orthodox semigroups /Marco Grandis. - Singapore ;World Scientific,c2012. - xi, 369 p. :ill. ;24 cm.

Includes bibliographical references (p. 357-361) and index.

Introduction --

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.

ISBN: 9789814407069 (hbk.) :US128.00

LCCN: 2012552090Subjects--Topical Terms:

663850
Algebra, Homological.

LC Class. No.: QA169 / .G73 2012

Dewey Class. No.: 512/.55

Homological algebra : = the interplay of homology with distributive lattices and orthodox semigroups /
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504 $a Includes bibliographical references (p. 357-361) and index.
505 0 # $t Introduction -- $t Coherence and models in homological algebra -- $t Puppe-exact categories -- $t Involutive categories -- $t Categories of relations as RE-categories -- $t Theories and models -- $t Homological theories and their universal models -- $t Appendix A : some points of category theory -- $t Appendix B : a proof for the universal exact system.
520 3 $a 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.
650 # 0 $a Algebra, Homological. $3 663850