Mathematical Sciences Classification System

18Axx - 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

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