Mathematics Subject Classification 1991

18-XX Category theory, homological algebra ( 0 Dok.)

• 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 18-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 18-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 18-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 18-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 18-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 18Axx General theory of categories and functors ( 0 Dok. )
• 18A05 Definitions, generalizations ( 0 Dok.)
• 18A10 Graphs, diagram schemes, precategories, neocategories, See also {20Lxx} ( 0 Dok.)
• 18A15 Foundations, relations to logic and deductive systems, See also {03-XX} ( 0 Dok.)
• 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms, factorization (bicategories) ( 0 Dok.)
• 18A22 Special properties of functors (faithful, full, etc.) ( 0 Dok.)
• 18A23 Natural morphisms, dinatural morphisms ( 0 Dok.)
• 18A25 Functor categories, comma categories ( 0 Dok.)
• 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) ( 0 Dok.)
• 18A32 Factorization of morphisms (via images, coimages, dominions, codominions), substructures, quotient structures, congruences, amalgams ( 0 Dok.)
• 18A35 Categories admitting limits (complete categories), functors commuting with limits, continuous functors, completions ( 0 Dok.)
• 18A40 Adjoint functors (representable functors, universal constructions, reflective subcategories, reflections, etc.), constructions of adjoints (Kan extensions, etc.) ( 0 Dok.)
• 18A99 None of the above but in this section ( 0 Dok.)
• 18Bxx Special categories ( 0 Dok. )
• 18B05 Category of sets, characterizations, See also {03-XX} ( 0 Dok.)
• 18B10 Category of relations, additive relations ( 0 Dok.)
• 18B15 Embedding theorems, universal categories, See also {18E20} ( 0 Dok.)
• 18B20 Categories of machines, automata, operative categories, See also {03D05, 68Qxx} ( 0 Dok.)
• 18B25 Topoi, See also {03G30} ( 0 Dok.)
• 18B30 Categories of topological spaces and continuous mappings, See also {54-XX} ( 0 Dok.)
• 18B35 Preorders, orders and lattices (viewed as categories), See also {06-XX} ( 0 Dok.)
• 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories), See also {20Axx, 20Lxx, 20Mxx} ( 0 Dok.)
• 18B99 None of the above but in this section ( 0 Dok.)
• 18Cxx Categories and algebraic theories ( 0 Dok. )
• 18C05 Equational categories, See also {03C05, 08C05} ( 0 Dok.)
• 18C10 Theories (e.g. algebraic theories), structure, and semantics, See also {03G30} ( 0 Dok.)
• 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples, See also {18Gxx} ( 0 Dok.)
• 18C20 Algebras and Kleisli categories associated with monads ( 0 Dok.)
• 18C99 None of the above but in this section ( 0 Dok.)
• 18Dxx Categories with structure ( 0 Dok. )
• 18D05 Double categories, $2$-categories, bicategories, hypercategories ( 0 Dok.)
• 18D10 Monoidal categories (= multiplicative categories), See also {19D23} ( 0 Dok.)
• 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) ( 0 Dok.)
• 18D20 Enriched categories (over closed or monoidal categories) ( 0 Dok.)
• 18D25 Strong functors, strong adjunctions ( 0 Dok.)
• 18D30 Fibered categories ( 0 Dok.)
• 18D35 Structured objects in a category (group objects, etc.) ( 0 Dok.)
• 18D99 None of the above but in this section ( 0 Dok.)
• 18Exx Abelian categories ( 0 Dok. )
• 18E05 Preadditive, additive categories ( 0 Dok.)
• 18E10 Exact categories, abelian categories ( 0 Dok.)
• 18E15 Grothendieck categories ( 0 Dok.)
• 18E20 Embedding theorems, See also {18B15} ( 0 Dok.)
• 18E25 Derived functors and satellites ( 0 Dok.)
• 18E30 Derived categories, triangulated categories ( 0 Dok.)
• 18E35 Localization of categories ( 0 Dok.)
• 18E40 Torsion theories, radicals, See also {13D30, 16S90} ( 0 Dok.)
• 18E99 None of the above but in this section ( 0 Dok.)
• 18Fxx Categories and geometry ( 0 Dok. )
• 18F05 Local categories and functors ( 0 Dok.)
• 18F10 Grothendieck topologies, See also {14F20} ( 0 Dok.)
• 18F15 Abstract manifolds and fiber bundles, See also {55Rxx, 57Pxx} ( 0 Dok.)
• 18F20 Presheaves and sheaves, See also {14F05, 32C35, 32L10, 54B40, 55N30} ( 0 Dok.)
• 18F25 Algebraic $K$-theory and $L$-theory, See also {11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67} ( 0 Dok.)
• 18F30 Grothendieck groups, See also {13D15, 16E20, 19Axx} ( 0 Dok.)
• 18F99 None of the above but in this section ( 0 Dok.)
• 18Gxx Homological algebra, See also {13Dxx, 16Exx, 55Uxx} ( 0 Dok. )
• 18G05 Projectives and injectives, See also {13C10, 13C11, 16D40, 16D50} ( 0 Dok.)
• 18G10 Resolutions; derived functors, See also {18E25} ( 0 Dok.)
• 18G15 Ext and Tor, generalizations, Kunneth formula, See Also { 55U25} ( 0 Dok.)
• 18G20 Homological dimension, See also {13D05, 16E10} ( 0 Dok.)
• 18G25 Relative homological algebra, projective classes ( 0 Dok.)
• 18G30 Simplicial sets, simplicial objects (in a category), See also {55U10} ( 0 Dok.)
• 18G35 Chain complexes, See also {18E30, 55U15} ( 0 Dok.)
• 18G40 Spectral sequences, hypercohomology, See also {55Txx} ( 0 Dok.)
• 18G50 Nonabelian homological algebra ( 0 Dok.)
• 18G55 Nonabelian homotopical algebra ( 0 Dok.)
• 18G60 Other (co)homology theories (cyclic, dihedral, etc.), See also {19D55, 46L80, 58B30, 58G12} ( 0 Dok.)
• 18G99 None of the above but in this section ( 0 Dok.)