La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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18-XX Category theory; homological algebra [For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology]

• 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 (must also be assigned at least one classification number from Section 01)
• 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)
• 18Axx General theory of categories and functors
• 18Bxx Special categories
• 18Cxx Categories and theories
• 18Dxx Categories with structure
• 18Exx Abelian categories
• 18Fxx 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
• 18Gxx Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]

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