Ýëåêòðîííàÿ áèáëèîòåêà Ïîïå÷èòåëüñêîãî ñîâåòàìåõàíèêî-ìàòåìàòè÷åñêîãî ôàêóëüòåòà Ìîñêîâñêîãî ãîñóäàðñòâåííîãî óíèâåðñèòåòà
 Ãëàâíàÿ    Ex Libris    Êíèãè    Æóðíàëû    Ñòàòüè    Ñåðèè    Êàòàëîã    Wanted    Çàãðóçêà    ÕóäËèò    Ñïðàâêà    Ïîèñê ïî èíäåêñàì    Ïîèñê    Ôîðóì
 Àâòîðèçàöèÿ Ïîèñê ïî óêàçàòåëÿì
Neeman A. — Triangulated categories
 Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå Íàøëè îïå÷àòêó?Âûäåëèòå åå ìûøêîé è íàæìèòå Ctrl+Enter Íàçâàíèå: Triangulated categories Àâòîð: Neeman A. Àííîòàöèÿ: The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories" — the "well generated triangulated categories" — and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics. ßçûê: Ðóáðèêà: Ìàòåìàòèêà/Àëãåáðà/Òåîðèÿ êàòåãîðèé/ Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2001 Êîëè÷åñòâî ñòðàíèö: 449 Äîáàâëåíà â êàòàëîã: 12.03.2005 Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
 Abelian categories of product-preserving functors      183—214 Abelian categories of product-preserving functors are locally presentable      221—224 326 Abelian categories of product-preserving functors do not satisfy [AB5], [AB5*]      209—210 Abelian categories of product-preserving functors have enough projectives      212 Abelian categories of product-preserving functors may not have cogenerators      403—405 Abelian categories of product-preserving functors satisfy [AB3*]      186—187 200 Abelian categories of product-preserving functors satisfy [AB3]      196—200 Abelian categories of product-preserving functors satisfy [AB4*]      206 Abelian categories of product-preserving functors satisfy [AB4]      207—209 Abelian categories of product-preserving functors via universal homological functor      384—385 Abelian categories of product-preserving functors, coproducts      191 Abelian categories of product-preserving functors, definitions      185 Abelian categories of product-preserving functors, homological functors      204—205 Abelian categories of product-preserving functors, homological objects      224—229 258—262 Abelian categories of product-preserving functors, homological objects, as filtered colimits of representables      226—229 Abelian categories of product-preserving functors, homological objects, characterisation in terms of vanishing Ext      258—259 Abelian categories of product-preserving functors, homological objects, Embedding arbitrary objects in homological ones      259—262 Abelian categories of product-preserving functors, homological objects, stable under filtered colimits      225 Abelian categories-review of formalism -filtered limits      321 Abelian categories-review of formalism -filtered limits, definition of [AB4.5()]      354 Abelian categories-review of formalism -filtered limits, definition of [AB5 ]      378 Abelian categories-review of formalism -filtered limits, derived functors of limit      345—361 Abelian categories-review of formalism -filtered limits, derived functors of limit, analogy with sheaves      349—351 Abelian categories-review of formalism -filtered limits, derived functors of limit, cofinal sequences      358 Abelian categories-review of formalism -filtered limits, derived functors of limit, flabby sequences      350 Abelian categories-review of formalism -filtered limits, derived functors of limit, Mittag — Leffler sequences      350—354 359—361 Abelian categories-review of formalism -filtered limits, derived functors of limit, sequences of length       348 Abelian categories-review of formalism -filtered limits, derived functors of limit, via canonical resolution      346—348 370—371 Abelian categories-review of formalism -filtered limits, derived functors of limit, via injectives      356 Abelian categories-review of formalism -filtered limits, injectives in functor categories      355—356 Abelian categories-review of formalism -filtered limits, local object      329 Abelian categories-review of formalism -filtered limits, localizant subcategory      328 Abelian categories-review of formalism -filtered limits, localizant subcategory, basic properties      332—334 Abelian categories-review of formalism -filtered limits, localizant subcategory, characterisations      334—335 338—339 Abelian categories-review of formalism -filtered limits, locally presentable categories      321 324—327 Abelian categories-review of formalism -filtered limits, quotient by Serre subcategory      327—328 Abelian categories-review of formalism -filtered limits, quotient maps and products      343—345 Abelian categories-review of formalism -filtered limits, quotients      327—345 Abelian categories-review of formalism -filtered limits, Serre subcategories      327 Abelian categories-review of formalism -filtered limits, [AB3* ()] and [AB4* ()]      346 Abelian categories-review of formalism -filtered limits, [AB3* ()] in functor categories      355 Abelian categories-review of formalism -filtered limits, [AB4] does not imply [AB4.5]      361—366 Adjoints of a triangulated functor is triangulated      179 Adjoints, A(-) preserves and reflects adjoints      181—182 Adjoints, Bousfield localisation      288 309—318 Adjoints, Brown representability      286—287 Bousfield localisation      288 309—318 Bousfield localisation for homology theory E      417—418 Bousfield localisation is selfdual      315—316 Bousfield localisation, embedding the quotient      316—317 Bousfield localisation, existence      288 318 Bousfield localisation, local object      310 Bousfield localisation, perpendicular subcategories      313 Brown representability      275 Brown representability for -perfectly generated categories      282—284 Brown representability for dual of E-acyclic spectra      419—420 Brown representability for duals of well-generated categories      303—306 Brown representability for E-acyclic spectra      417—418 Brown representability for E-local spectra      417—418 Brown representability for spectra      408 Brown representability for well-generated categories      285—286 Brown representability, adjoints      286 Brown — Comenetz objects      302—303 307 Cardinal of       410—411 Cardinal, regular      103 Cardinal, singular      103 Cofinal sequences      358 Compact generating set      274 Compact objects      130 Compact objects in quotient      138 143—144 Compact objects, filtrations by coproducts      371—378 Compact objects, generators for      140 Compact objects, subcategory of      129 Compact objects, subcategory of, inclusion relations      129 Compact objects, subcategory of, is localising      130 Compactly generated categories      274 Existence of products      288 Filtrations by coproducts of compact objects      371—378 Freyd's universal abelian category      153—182 Freyd's universal abelian category, is a Frobenius category      169 Freyd's universal abelian category, is an abelian subcategory closed under extensions      161 Freyd's universal abelian category, A(-) is a functor, and preserves products      177—179 Freyd's universal abelian category, A(-) is a functor, and preserves products, is a Frobenius category      169 Freyd's universal abelian category, A(-) is a functor, and preserves products, is an abelian subcategory closed under extensions      161 Freyd's universal abelian category, A(-) is a functor, and preserves products, A(-) preserves and reflects adjoints      181—182 Freyd's universal abelian category, A(-) is a functor, and preserves products, category and its equivalence with       162—163 Freyd's universal abelian category, A(-) is a functor, and preserves products, category and its equivalence with       167—169 Freyd's universal abelian category, A(-) is a functor, and preserves products, category and its equivalence with       172—173 Freyd's universal abelian category, A(-) is a functor, and preserves products, coproducts in when satisfies [TR5]      169—171 Freyd's universal abelian category, A(-) is a functor, and preserves products, definition of       154 Freyd's universal abelian category, A(-) is a functor, and preserves products, example of non-well-powered      394 Freyd's universal abelian category, A(-) is a functor, and preserves products, functors in preserve products      154 Freyd's universal abelian category, A(-) is a functor, and preserves products, relation with , Ab      214—220 Freyd's universal abelian category, A(-) is a functor, and preserves products, subobjects and quotient objects      172—177 Freyd's universal abelian category, A(-) is a functor, and preserves products, universal homological functor      163—164 Freyd's universal abelian category, A(-) preserves and reflects adjoints      181—182 Freyd's universal abelian category, category and its equivalence with       162—163 Freyd's universal abelian category, category and its equivalence with       167—169 Freyd's universal abelian category, category and its equivalence with       172—173 Freyd's universal abelian category, coproducts in when satisfies [TR5]      169—171 Freyd's universal abelian category, definition of       154 Freyd's universal abelian category, example of non-well-powered      394 Freyd's universal abelian category, functors in preserve products      154 Freyd's universal abelian category, have enough projectives      153—154 Freyd's universal abelian category, relation with , Ab      214—220 Freyd's universal abelian category, subobjects and quotient objects      172—177 Freyd's universal abelian category, universal homological functor      163—164 Functor , Ab is exact and respects coproducts      215 Functor , Ab is restriction      215—216 Functor , Ab is the quotient by a colocalizant subcategory      216—218 290 Functor , Ab is the quotient by a localizant subcategory in the presence of injectives      289—290 Functor , Ab, existence      214—215 Functor , Ab, respects products      218 Functor categories, abelian categories of product-preserving functors      183—214 Functor categories, abelian categories of product-preserving functors, are locally presentable      221—224 326 Functor categories, abelian categories of product-preserving functors, coproducts      191 Functor categories, abelian categories of product-preserving functors, definitions      185 Functor categories, abelian categories of product-preserving functors, do not satisfy [AB5], [AB5*]      209—210 Functor categories, abelian categories of product-preserving functors, Embedding arbitrary objects in homological ones      259—262 Functor categories, abelian categories of product-preserving functors, have enough projectives      212 Functor categories, abelian categories of product-preserving functors, homological functors      204—205 Functor categories, abelian categories of product-preserving functors, homological objects      224—229 258—262 Functor categories, abelian categories of product-preserving functors, homological objects characterised in terms of vanishing Ext      258—259 Functor categories, abelian categories of product-preserving functors, may not have cogenerators      403—405 Functor categories, abelian categories of product-preserving functors, relation with Freyd's universal abelian category      214—220 Functor categories, abelian categories of product-preserving functors, satisfy [AB3*]      186—187 200 Functor categories, abelian categories of product-preserving functors, satisfy [AB3]      196—200 Functor categories, abelian categories of product-preserving functors, satisfy [AB4*]      206 Functor categories, abelian categories of product-preserving functors, satisfy [AB4]      207—209 Functor categories, abelian categories of product-preserving functors, via universal homological functor      384—385 Functor, kernel of      74 99 Functor, representability      275 Functor, representability, for -perfectly generated categories      282—284 Functor, representability, for duals of well-generated categories      303—306 Functor, representability, for well-generated categories      285—286 Functor, triangulated      73 Generating set      205 273—274 Generating set a category without      438—441 Generating set in the dual of well-generated categories      302—303 Generating set, compact      274 Generating set, compactly generated categories      274 Generating set, generate category      285 Generating set, perfect      273—274 Generating set, well generated categories      274 Gluing data      318—319 Good morhism of triangles      52 Good object in a subcategory      113 Grothendieck's duality theorem      306 Homological functor as object in , Ab      224—229 258—262 Homological functor as object in , Ab, as filtered colimits of representables      226—229 Homological functor as object in , Ab, characterisation in terms of vanishing Ext      258—259 Homological functor as object in , Ab, Embedding arbitrary objects in homological ones      259—262 Homological functor as object in , Ab, stable under filtered colimits      225 Homological functor into abelian functor categories      204—205 Homological functor, definition      32 Homological functor, examples      32 Homological functor, universal      163—166 Homological functor, universal into [AB5*]      384—385 Homotopy cartesian square      52 Homotopy colimits of subsequences      68—70 Homotopy colimits, definition      63 Homotopy colimits, elementary properties      64—65 Homotopy pullback      54—55 183—184 Homotopy pushout      53—54 Idempotent splitting      65 Kernel of functor      74 99 Large categories      99—100 Limits -filtered      321 Local object in abelian category      329 Local object in triangulated category      310 Localisation, Bousfield      288 309—318 Localisation, Bousfield, embedding the quotient      316—317 Localisation, Bousfield, existence      288 318 Localisation, Bousfield, is selfdual      315—316 Localisation, Bousfield, local object      310 Localisation, Bousfield, perpendicular subcategories      313 Localisation, Thomason      143—144 Localisation, Verdier      74—99 309 Localisation, Verdier, existence theorem      74—75 Localisation, Verdier, size of Hom-sets      99—100 137 318 Localising subcategory      106—107 Localising subcategory of small objects      126 Locally presentable categories      221—224 321 324—327 Mapping cone, definition      45 Mapping cone, [TR4]      51 Modules , definition      387—388 Modules , force large images      391 Modules , respect homomorphisms      390—391 Modules , stabilise eventually      390 Octahedral axiom      58 60 Perfect classes, definition      110—111 Perfect classes, maximal      120—121 Perfect classes, new out of old      111 116 119 Perfect classes, which are triangulated subcategories      115 Perfect generating set      273—274 Perfectly generated category      274 Perfectly generated category, is not      432—437 Phantom maps      219—220 Phantom maps and injectives in , Ab      299—300 Phantom maps and right adjoint to       301 Phantom maps annihilated by homological functors into [AB5*] categories      383—384 Phantom maps as the kernel of , Ab      218—219 Phantom maps from coproducts of compacts vanish      369—370 Phantom maps in       438—440 Phantom maps, definition      219 Phantom maps, existence for every       219—220 Pretriangle, definition      33 Pretriangle, examples      34 Pretriangle, new out of old      34 49 Pretriangulated category      29 70 Pretriangulated category, definition      29 Products of triangles are triangles      37 Products, existence of      288 Quotient categories      74—99 309 Quotient categories, commutative squares      85—86 Quotient categories, compact objects      143—144 Quotient categories, embedding via Bousfield localisation      316—317 Quotient categories, equality of morphisms      84—85 Quotient categories, existence      74—75 84 Quotient categories, isomorphisms      90 92 Quotient categories, preservation of products      107 110 Quotient categories, size of Hom-sets      99—100 137 318 Quotient categories, zero objects      91 Regular cardinal      103 Representability of functors      275 Representability of functors for -perfectly generated categories      282—284 Representability of functors for duals of well-generated categories      303—306 Representability of functors for well-generated categories      285—286 Serre subcategories      327 Singular cardinal      103 Six functors      318—319 Small categories      99—100 137 Small hom-sets      99—100 137 318 Small object, definition      123 Small object, subcategory of      124 Small object, subcategory of, is localising      126 Small object, subcategory of, is triangulated      124 Spectra, , Ab does not have a cogenerator      425 Spectra, Bousfield localisation for homology      417—418 Spectra, Brown representability      408 Spectra, cardinal of       410—411 Spectra, E-acyclics      411—412 Spectra, E-acyclics, are well-generated      417—418 Spectra, E-acyclics, Brown representability      417—418 Spectra, E-acyclics, Brown representability for dual      419—420 Spectra, E-local      419 Spectra, E-local, are well-generated      417—418 Spectra, E-local, Brown representability      417—418 Spectra, elementary properties      407—408 Spectra, functor to D(R)      420 Spectra, functor to D(R), descends to , Ab      422—425 Spectra, functor to D(R), respects -compacts      420—421 Splitting, idempotent      65 Splitting, triangle with 0      42—45 Subcategory of compact objects      129 130 Subcategory of compact objects, inclusion relations      129 Subcategory of compact objects, is localising      130 Subcategory of small objects      124 Subcategory of small objects is localising      126 Subcategory of small objects is triangulated      124 Subcategory, generated by a set      103—104 106—107 Subcategory, localising      106—107 Subcategory, thick      74 99 Subcategory, thick closure      75 99 147—149 Subcategory, triangulated      60 Thomason localisation      143—144 Thomason localisation, applied to finding       409 TR0      29 TR1      29 TR2      29 TR3      30 TR4, equivalent formulations      51 60 TR5, dual      63 TR5, statement      63 Triangles, contractible      47 48 Triangles, distinguished      29 Triangles, products of      37 Triangles, summands of      38 Triangulated subcategories, which are perfect classes      115 Universal homological functors      163—166 384—385 Verdier localisation      74—99 309 Verdier localisation, existence theorem      74—75 Verdier localisation, size of Hom-sets      99—100 137 318 Well generated categories      274 Well generated categories are unions of       285—286 Well generated categories, duals satisfy Brown representability      303—306 Well generated categories, neither nor       437—441 Well generated categories, not both T and T op      427—431 Well generated categories, satisfy Brown representability      285—286
Ðåêëàìà
 © Ýëåêòðîííàÿ áèáëèîòåêà ïîïå÷èòåëüñêîãî ñîâåòà ìåõìàòà ÌÃÓ, 2004-2022 | | Î ïðîåêòå