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Mathematics Subject Classification 1991
18-XX Category theory, homological algebra
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18-00
General reference works (handbooks, dictionaries, bibliographies, etc.)
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18-01
Instructional exposition (textbooks, tutorial papers, etc.)
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18-02
Research exposition (monographs, survey articles)
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18-03
Historical (must be assigned at least one classification number from Section 01)
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18-04
Explicit machine computation and programs (not the theory of computation or programming)
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18-06
Proceedings, conferences, collections, etc.
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18Axx General theory of categories and functors
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18A05
Definitions, generalizations
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18A10
Graphs, diagram schemes, precategories, neocategories, See also {20Lxx}
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18A15
Foundations, relations to logic and deductive systems, See also {03-XX}
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18A20
Epimorphisms, monomorphisms, special classes of morphisms, null morphisms, factorization (bicategories)
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18A22
Special properties of functors (faithful, full, etc.)
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18A23
Natural morphisms, dinatural morphisms
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18A25
Functor categories, comma categories
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18A30
Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
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18A32
Factorization of morphisms (via images, coimages, dominions, codominions), substructures, quotient structures, congruences, amalgams
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18A35
Categories admitting limits (complete categories), functors commuting with limits, continuous functors, completions
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18A40
Adjoint functors (representable functors, universal constructions, reflective subcategories, reflections, etc.), constructions of adjoints (Kan extensions, etc.)
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18A99
None of the above but in this section
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18Bxx Special categories
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18B05
Category of sets, characterizations, See also {03-XX}
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18B10
Category of relations, additive relations
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18B15
Embedding theorems, universal categories, See also {18E20}
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18B20
Categories of machines, automata, operative categories, See also {03D05, 68Qxx}
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18B25
Topoi, See also {03G30}
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18B30
Categories of topological spaces and continuous mappings, See also {54-XX}
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18B35
Preorders, orders and lattices (viewed as categories), See also {06-XX}
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18B40
Groupoids, semigroupoids, semigroups, groups (viewed as categories), See also {20Axx, 20Lxx, 20Mxx}
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18B99
None of the above but in this section
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18Cxx Categories and algebraic theories
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18C05
Equational categories, See also {03C05, 08C05}
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18C10
Theories (e.g. algebraic theories), structure, and semantics, See also {03G30}
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18C15
Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples, See also {18Gxx}
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18C20
Algebras and Kleisli categories associated with monads
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18C99
None of the above but in this section
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18Dxx Categories with structure
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18D05
Double categories, $2$-categories, bicategories, hypercategories
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18D10
Monoidal categories (= multiplicative categories), See also {19D23}
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18D15
Closed categories (closed monoidal and Cartesian closed categories, etc.)
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18D20
Enriched categories (over closed or monoidal categories)
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18D25
Strong functors, strong adjunctions
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18D30
Fibered categories
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18D35
Structured objects in a category (group objects, etc.)
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18D99
None of the above but in this section
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18Exx Abelian categories
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18E05
Preadditive, additive categories
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18E10
Exact categories, abelian categories
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18E15
Grothendieck categories
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18E20
Embedding theorems, See also {18B15}
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18E25
Derived functors and satellites
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18E30
Derived categories, triangulated categories
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18E35
Localization of categories
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18E40
Torsion theories, radicals, See also {13D30, 16S90}
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18E99
None of the above but in this section
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18Fxx Categories and geometry
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18F05
Local categories and functors
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18F10
Grothendieck topologies, See also {14F20}
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18F15
Abstract manifolds and fiber bundles, See also {55Rxx, 57Pxx}
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18F20
Presheaves and sheaves, See also {14F05, 32C35, 32L10, 54B40, 55N30}
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18F25
Algebraic $K$-theory and $L$-theory, See also {11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67}
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18F30
Grothendieck groups, See also {13D15, 16E20, 19Axx}
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18F99
None of the above but in this section
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18Gxx Homological algebra, See also {13Dxx, 16Exx, 55Uxx}
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18G05
Projectives and injectives, See also {13C10, 13C11, 16D40, 16D50}
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18G10
Resolutions; derived functors, See also {18E25}
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18G15
Ext and Tor, generalizations, Kunneth formula, See Also { 55U25}
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18G20
Homological dimension, See also {13D05, 16E10}
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18G25
Relative homological algebra, projective classes
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18G30
Simplicial sets, simplicial objects (in a category), See also {55U10}
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18G35
Chain complexes, See also {18E30, 55U15}
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18G40
Spectral sequences, hypercohomology, See also {55Txx}
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18G50
Nonabelian homological algebra
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18G55
Nonabelian homotopical algebra
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18G60
Other (co)homology theories (cyclic, dihedral, etc.), See also {19D55, 46L80, 58B30, 58G12}
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18G99
None of the above but in this section
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Letzte Änderung: 10. Nov. 2010