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Mathematical Sciences Classification System

18Axx - General theory of categories and functors

• 18A05
  Definitions, generalizations
• 1
  18A10
  Graphs, diagram schemes, precategories [See especially 20L05]
• 4
  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
• 3
  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
• 3
  18A40
  Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
• 1
  18A99
  None of the above, but in this section