Homological algebra: the interplay of homology with distributive lattices and orthodox semigroups
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...
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2012
|
Schlagworte: | |
Online-Zugang: | FHN01 Volltext |
Zusammenfassung: | 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 |
Beschreibung: | xi, 369 p. ill |
ISBN: | 9789814407076 |
Internformat
MARC
LEADER | 00000nmm a2200000zc 4500 | ||
---|---|---|---|
001 | BV044638933 | ||
003 | DE-604 | ||
005 | 00000000000000.0 | ||
007 | cr|uuu---uuuuu | ||
008 | 171120s2012 |||| o||u| ||||||eng d | ||
020 | |a 9789814407076 |c electronic bk. |9 978-981-4407-07-6 | ||
024 | 7 | |a 10.1142/8483 |2 doi | |
035 | |a (ZDB-124-WOP)00002746 | ||
035 | |a (OCoLC)1012663376 | ||
035 | |a (DE-599)BVBBV044638933 | ||
040 | |a DE-604 |b ger |e aacr | ||
041 | 0 | |a eng | |
049 | |a DE-92 | ||
082 | 0 | |a 512.64 |2 22 | |
084 | |a SK 320 |0 (DE-625)143231: |2 rvk | ||
100 | 1 | |a Grandis, Marco |e Verfasser |4 aut | |
245 | 1 | 0 | |a Homological algebra |b the interplay of homology with distributive lattices and orthodox semigroups |c Marco Grandis |
264 | 1 | |a Singapore |b World Scientific Pub. Co. |c c2012 | |
300 | |a xi, 369 p. |b ill | ||
336 | |b txt |2 rdacontent | ||
337 | |b c |2 rdamedia | ||
338 | |b cr |2 rdacarrier | ||
520 | |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 | 4 | |a Algebra, Homological | |
650 | 4 | |a Lattices, Distributive | |
650 | 0 | 7 | |a Homologische Algebra |0 (DE-588)4160598-6 |2 gnd |9 rswk-swf |
689 | 0 | 0 | |a Homologische Algebra |0 (DE-588)4160598-6 |D s |
689 | 0 | |8 1\p |5 DE-604 | |
776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9789814407069 |
776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9814407062 |
856 | 4 | 0 | |u http://www.worldscientific.com/worldscibooks/10.1142/8483#t=toc |x Verlag |z URL des Erstveroeffentlichers |3 Volltext |
912 | |a ZDB-124-WOP | ||
999 | |a oai:aleph.bib-bvb.de:BVB01-030036905 | ||
883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
966 | e | |u http://www.worldscientific.com/worldscibooks/10.1142/8483#t=toc |l FHN01 |p ZDB-124-WOP |q FHN_PDA_WOP |x Verlag |3 Volltext |
Datensatz im Suchindex
_version_ | 1804178056369143808 |
---|---|
any_adam_object | |
author | Grandis, Marco |
author_facet | Grandis, Marco |
author_role | aut |
author_sort | Grandis, Marco |
author_variant | m g mg |
building | Verbundindex |
bvnumber | BV044638933 |
classification_rvk | SK 320 |
collection | ZDB-124-WOP |
ctrlnum | (ZDB-124-WOP)00002746 (OCoLC)1012663376 (DE-599)BVBBV044638933 |
dewey-full | 512.64 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512.64 |
dewey-search | 512.64 |
dewey-sort | 3512.64 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Electronic eBook |
fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03156nmm a2200445zc 4500</leader><controlfield tag="001">BV044638933</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">171120s2012 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814407076</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-981-4407-07-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1142/8483</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-124-WOP)00002746</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1012663376</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044638933</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.64</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 320</subfield><subfield code="0">(DE-625)143231:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Grandis, Marco</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Homological algebra</subfield><subfield code="b">the interplay of homology with distributive lattices and orthodox semigroups</subfield><subfield code="c">Marco Grandis</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore</subfield><subfield code="b">World Scientific Pub. Co.</subfield><subfield code="c">c2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xi, 369 p.</subfield><subfield code="b">ill</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra, Homological</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lattices, Distributive</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Homologische Algebra</subfield><subfield code="0">(DE-588)4160598-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Homologische Algebra</subfield><subfield code="0">(DE-588)4160598-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9789814407069</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9814407062</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/8483#t=toc</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveroeffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-124-WOP</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030036905</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/8483#t=toc</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-124-WOP</subfield><subfield code="q">FHN_PDA_WOP</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
id | DE-604.BV044638933 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:57:54Z |
institution | BVB |
isbn | 9789814407076 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030036905 |
oclc_num | 1012663376 |
open_access_boolean | |
owner | DE-92 |
owner_facet | DE-92 |
physical | xi, 369 p. ill |
psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
publishDate | 2012 |
publishDateSearch | 2012 |
publishDateSort | 2012 |
publisher | World Scientific Pub. Co. |
record_format | marc |
spelling | Grandis, Marco Verfasser aut Homological algebra the interplay of homology with distributive lattices and orthodox semigroups Marco Grandis Singapore World Scientific Pub. Co. c2012 xi, 369 p. ill txt rdacontent c rdamedia cr rdacarrier 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 Algebra, Homological Lattices, Distributive Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9789814407069 Erscheint auch als Druck-Ausgabe 9814407062 http://www.worldscientific.com/worldscibooks/10.1142/8483#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Grandis, Marco Homological algebra the interplay of homology with distributive lattices and orthodox semigroups Algebra, Homological Lattices, Distributive Homologische Algebra (DE-588)4160598-6 gnd |
subject_GND | (DE-588)4160598-6 |
title | Homological algebra the interplay of homology with distributive lattices and orthodox semigroups |
title_auth | Homological algebra the interplay of homology with distributive lattices and orthodox semigroups |
title_exact_search | Homological algebra the interplay of homology with distributive lattices and orthodox semigroups |
title_full | Homological algebra the interplay of homology with distributive lattices and orthodox semigroups Marco Grandis |
title_fullStr | Homological algebra the interplay of homology with distributive lattices and orthodox semigroups Marco Grandis |
title_full_unstemmed | Homological algebra the interplay of homology with distributive lattices and orthodox semigroups Marco Grandis |
title_short | Homological algebra |
title_sort | homological algebra the interplay of homology with distributive lattices and orthodox semigroups |
title_sub | the interplay of homology with distributive lattices and orthodox semigroups |
topic | Algebra, Homological Lattices, Distributive Homologische Algebra (DE-588)4160598-6 gnd |
topic_facet | Algebra, Homological Lattices, Distributive Homologische Algebra |
url | http://www.worldscientific.com/worldscibooks/10.1142/8483#t=toc |
work_keys_str_mv | AT grandismarco homologicalalgebratheinterplayofhomologywithdistributivelatticesandorthodoxsemigroups |