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Biblioteca Dr. Antonio Monteiro · Catálogo |
| 18 | Category theory; homological algebra | ||
| 18-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) | ||
| 18-01 | Instructional exposition (textbooks, tutorial papers, etc.) | ||
| 18-02 | Research exposition (monographs, survey articles) | ||
| 18-03 | Historical | ||
| 18-04 | Explicit machine computation and programs (not the theory of computation or programming) | ||
| 18-06 | Proceedings, conferences, collections, etc. | ||
| 18-99 | Category theory; homological algebra (not classified at a more specific level) | ||
| 18A | General theory of categories and functors | ||
| 18A05 | Definitions, generalizations | ||
| 18A10 | Graphs, diagram schemes, precategories [See especially 20L05] | ||
| 18A15 | Foundations, relations to logic and deductive systems [See also 03-XX] | ||
| 18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms | ||
| 18A22 | Special properties of functors (faithful, full, etc.) | ||
| 18A23 | Natural morphisms, dinatural morphisms | ||
| 18A25 | Functor categories, comma categories | ||
| 18A30 | Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) | ||
| 18A32 | Factorization of morphisms, substructures, quotient structures, congruences, amalgams | ||
| 18A35 | Categories admitting limits (complete categories), functors preserving limits, completions | ||
| 18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) | ||
| 18A99 | None of the above, but in this section | ||
| 18B | Special categories | ||
| 18B05 | Category of sets, characterizations [See also 03-XX] | ||
| 18B10 | Category of relations, additive relations | ||
| 18B15 | Embedding theorems, universal categories [See also 18E20] | ||
| 18B20 | Categories of machines, automata, operative categories [See also 03D05, 68Qxx] | ||
| 18B25 | Topoi [See also 03G30] | ||
| 18B30 | Categories of topological spaces and continuous mappings [See also 54-XX] | ||
| 18B35 | Preorders, orders and lattices (viewed as categories) [See also 06-XX] | ||
| 18B40 | Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] | ||
| 18B99 | None of the above, but in this section | ||
| 18C | Categories and theories | ||
| 18C05 | Equational categories [See also 03C05, 08C05] | ||
| 18C10 | Theories (e.g. algebraic theories), structure, and semantics [See also 03G30] | ||
| 18C15 | Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx] | ||
| 18C20 | Algebras and Kleisli categories associated with monads | ||
| 18C30 | Sketches and generalizations | ||
| 18C35 | Accessible and locally presentable categories | ||
| 18C50 | Categorical semantics of formal languages [See also 68Q55, 68Q65] | ||
| 18C99 | None of the above, but in this section | ||
| 18D | Categories with structure | ||
| 18D05 | Double categories, $2$-categories, bicategories and generalizations | ||
| 18D10 | Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] | ||
| 18D15 | Closed categories (closed monoidal and Cartesian closed categories, etc.) | ||
| 18D20 | Enriched categories (over closed or monoidal categories) | ||
| 18D25 | Strong functors, strong adjunctions | ||
| 18D30 | Fibered categories | ||
| 18D35 | Structured objects in a category (group objects, etc.) | ||
| 18D50 | Operads [See also 55P48] | ||
| 18D99 | None of the above, but in this section | ||
| 18E | Abelian categories | ||
| 18E05 | Preadditive, additive categories | ||
| 18E10 | Exact categories, abelian categories | ||
| 18E15 | Grothendieck categories | ||
| 18E20 | Embedding theorems [See also 18B15] | ||
| 18E25 | Derived functors and satellites | ||
| 18E30 | Derived categories, triangulated categories | ||
| 18E35 | Localization of categories | ||
| 18E40 | Torsion theories, radicals [See also 13D30, 16S90] | ||
| 18E99 | None of the above, but in this section | ||
| 18F | Categories and geometry | ||
| 18F05 | Local categories and functors | ||
| 18F10 | Grothendieck topologies [See also 14F20] | ||
| 18F15 | Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx] | ||
| 18F20 | Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30] | ||
| 18F25 | Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] | ||
| 18F30 | Grothendieck groups [See also 13D15, 16E20, 19Axx] | ||
| 18F99 | None of the above, but in this section | ||
| 18G | Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx] | ||
| 18G05 | Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50] | ||
| 18G10 | Resolutions; derived functors [See also 13D02, 16E05, 18E25] | ||
| 18G15 | Ext and Tor, generalizations, Künneth formula [See also 55U25] | ||
| 18G20 | Homological dimension [See also 13D05, 16E10] | ||
| 18G25 | Relative homological algebra, projective classes | ||
| 18G30 | Simplicial sets, simplicial objects (in a category) [See also 55U10] | ||
| 18G35 | Chain complexes [See also 18E30, 55U15] | ||
| 18G40 | Spectral sequences, hypercohomology [See also 55Txx] | ||
| 18G50 | Nonabelian homological algebra | ||
| 18G55 | Homotopical algebra | ||
| 18G60 | Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22] | ||
| 18G99 | None of the above, but in this section | ||
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