From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7354 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: A book on Homological Algebra Date: Mon, 25 Jun 2012 09:29:40 +0200 Message-ID: Reply-To: Marco Grandis NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=WINDOWS-1252; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1340631223 7578 80.91.229.3 (25 Jun 2012 13:33:43 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 25 Jun 2012 13:33:43 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Mon Jun 25 15:33:38 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Sj9Q8-0001zl-SK for gsmc-categories@m.gmane.org; Mon, 25 Jun 2012 15:33:37 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51057) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Sj9Pb-0004pJ-UD; Mon, 25 Jun 2012 10:33:03 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Sj9Pb-0005vM-UB for categories-list@mlist.mta.ca; Mon, 25 Jun 2012 10:33:03 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7354 Archived-At: The following book has been published at World Scientific; below there is a copy of its presentation in the WS web page. Best regards to colleagues and friends Marco Grandis _____________________________________________________________ HOMOLOGICAL ALGEBRA The Interplay of Homology with Distributive Lattices and Orthodox =20 Semigroups by Marco Grandis World Scientific Publishing Co., 384pp General information: http://www.worldscibooks.com/mathematics/=20 8483.html Table of Contents (45k): http://www.worldscibooks.com/etextbook/=20 8483/8483_toc.pdf Preface (37k): http://www.worldscibooks.com/etextbook/=20 8483/8483_preface.pdf Introduction (123k): http://www.worldscibooks.com/etextbook/=20 8483/8483_intro.pdf Chapter 1: Coherence and models in homological algebra (333k): =20 http://www.worldscibooks.com/etextbook/8483/8483_chap01.pdf In this book we want to explore aspects of coherence in homological =20 algebra, that already appear in the classical situation of abelian =20 groups or abelian categories. Lattices of subobjects are shown to play an important role in the =20 study of homological systems, from simple chain complexes to all the =20 structures that give rise to spectral sequences. A parallel role is =20 played by semigroups of endorelations. These links rest on the fact that many such systems, but not all of =20 them, live in distributive sublattices of the modular lattices of =20 subobjects of the system. The property of distributivity allows one to work with induced =20 morphisms in an automatically consistent way, as we prove in a =20 =91Coherence Theorem for homological algebra=92. (On the contrary, a = =91non-=20 distributive=92 homological structure like the bifiltered chain complex =20= can easily lead to inconsistency, if one explores the interaction of =20 its two spectral sequences farther than it is normally done.) The same property of distributivity also permits representations of =20 homological structures by means of sets and lattices of subsets, =20 yielding a precise foundation for the heuristic tool of Zeeman =20 diagrams as universal models of spectral sequences. We thus establish an effective method of working with spectral =20 sequences, called =91crossword chasing=92, that can often replace the =20= usual complicated algebraic tools and be of much help to readers that =20= want to apply spectral sequences in any field. 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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]