书籍简介:

本书是一本非常有价值的专著/教科书，无其他书可替代。既给出了最基本的原始思想，又逐步深入直至最新的发展。这是一本内容非常全面的参考书，且该书的作者是该领域的权威。

书籍目录:

Ⅰ.SimplicialSets

Ⅰ.1TriangulatedSpaces

Ⅰ.2SimplicialSets

Ⅰ.3SimplicialTopologicalSpacesandtheEilenberg-ZilberTheorem

Ⅰ.4HomologyandCohmology

Ⅰ.5Sheaves

Ⅰ.6TheExactSequence

Ⅰ.7Complexes

Ⅱ.MainNotionsoftheCategoryTheory

Ⅱ.1TheLanguageofCategoriesandFunctors

Ⅱ.2CategoriesandStructures,EquivalenceofCategories

Ⅱ.3StructuresandCategories.RepresentableFunctors

Ⅱ.4CategoryApproachtotheConstructionofGeometricalObjects

Ⅱ.5AdditiveandAbelianCategories

Ⅱ.6FunctorsinAbelianCategories

Ⅲ.DerivedCategoriesandDerivedFunctors

Ⅲ.1ComplexesasGeneralizedObjects

Ⅲ.2DerivedCategoriesandLocalization

Ⅲ.3TrianglesasGeneralizedExactTriples

Ⅲ.4DerivedCategoryastheLocalizationofHomotopicCategory

Ⅲ.5TheStructureoftheDerivedCategory

Ⅲ.6DerivedFunctors

Ⅲ.7DerivedFunctoroftheComposition.SpectralSequence

Ⅲ.8SheafCohomology

Ⅳ.TriangulatedCategories

Ⅳ.1TriangulatedCategories

Ⅳ.2DerivedCategoriesAreTriangulated

Ⅳ.3AnExample:TheTriangulatedCategoryofA-Modules

Ⅳ.4Cores

Ⅴ.IntroductiontoHomotopicAlgebra

Ⅴ.1ClosedModelCategories

Ⅴ.2HomotopicCharacterizationofWeakEquivalences.

Ⅴ.3DG-AlgebrasasaClosedModelCategory

Ⅴ.4MinimalAlgebras

Ⅴ.5EquivalenceofHomotopyCategories

References

Index

内容摘要:

　　Inthesecondeditionofourbook,manyofthetypos,errors,andimprecisestatementsthatfoundtheirwayintothefirstedition,arecorrected.TheauthorsareextremelygratefultoProfessorSergeiMerkulovwhotookuponhimselfthedifficulttaskofcarefullyreadingthetextandincorporatingappropriatechanges.Withouthisefforts,mostoftheerrorsinthefirsteditionwouldprobablyhaveremainedunnoticed.Ofcourse,theauthorsretainfullresponsibilityforanymistakesthatmaystillremaininthetext.　　Homologicalalgebrafirstaroseasalanguagefordescribingtopologicalprospectsofgeometricalobjects.Aswitheverysuccessfullanguageitquicklyexpandeditscoverageandsemantics,anditscontemporaryapplicationsaremanyanddiverse.Thismodernapproachtohomologicalalgebra,bytwoleadingwritersinthefield,isbasedonthesystematicuseofthelanguageandideasofderivedcategoriesandderivedfunctors.Relationswithstandardcohomologytheory(sheafcohomology,spectralsequences,etc.)aredescribed.Inmostcasescompleteproofsaregiven.Basicconceptsandresultsofhomotopicalalgebraarealsopresented.Thebookaddressespeoplewhowanttolearnamodernapproachtohomologicalalgebraandtouseitintheirwork.Forthesecondeditiontheauthorshavemadenumerouscorrections.

书籍规格:

书籍详细信息
书名	同调代数方法：第2版站内查询相似图书
丛书名	国外数学名著系列
	9787030234810 如需购买下载《同调代数方法：第2版》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN
出版地	北京	出版单位	科学出版社
版次	影印本	印次	1
定价(元)	88.0	语种	英文
尺寸	24	装帧	精装
页数		印数

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书籍信息归属:

同调代数方法：第2版是科学出版社于2008.出版的中图分类号为 O154 的主题关于同调代数－英文的书籍。