nLab Mathematics Subject Classification

The American Mathematical Society’s Mathematics Subject Classification (MSC) is a classification system for subjects of mathematics.

• mathscinet.ams.org/msc/msc2020.html

Each code consists of three parts; the first two digits denote the broadest discipline of the subject. The following one digit denotes the narrower topic, while the last two digits denote the most specific subject.

Examples

A few examples are listed below based on MSC2020. Each discipline and topic, if appropriate, is linked to a corresponding article.

• 03-XX: mathematical logic and foundations
  • 03Bxx: General logic
    • 03B16: higher-order logic
    • 03B38: type theory
• 18-XX: category theory, homological algebra
  • 18Axx: general theory of categories and functors
    • 18A20: epimorphism, monomorphism, other morphisms, zero morphism
    • 18A25: functor category, comma category
    • 18A40: adjoint functor
  • 18Bxx: special categories
    • 18B25: topoi
    • 18A30: limit and colimit (product and coproduct, pullback and pushout, equalizer and coequalizer, kernel and cokernel, end and coend)
    • 18B40: groupoid, semigroupoid, semigroup, group
  • 18Dxx: categorical structures
    • 18D20: enriched category
    • 18D70: formal category theory
  • 18Exx: categorical algebra
    • 18E05: preadditive category, additive category
    • 18E08: regular category, Barr-exact category
    • 18E10: abelian category, Grothendieck category
    • 18E13: protomodular category, semi-abelian category, Malcev category
    • 18E35: category of fractions, calculus of fractions
  • 18Fxx: categories in geometry and topology
    • 18F10: Grothendieck topology, Grothendieck topos
    • 18F20: presheaf, sheaf, stack, descent
    • 18F30: Grothendieck group
    • 18F40: synthetic differential geometry, tangent category, differential category
    • 18F50: Goodwillie calculus, functor calculus
    • 18F70: frame, locale, point-free topology, Stone duality
    • 18F75: quantale
  • 18Gxx: homological algebra in category theory, derived categories and functors
    • 18G10: resolution, derived functor
    • 18G35: chain complex, dg-category
    • 18G50: nonabelian homological algebra
    • 18G70: $A_\infty$-category, relations with homological mirror symmetry
    • 18G80: derived category, triangulated category
    • 18G85: graph complex, graph homology
  • 18Mxx: monoidal categories and operads
    • 18M05: monoidal category, symmetric monoidal category
    • 18M10: traced monoidal category, compact closed category, star-autonomous category
    • 18M15: braided monoidal category, ribbon category
    • 18M20: fusion category, modular tensor category, modular functor
    • 18M25: Tannakian category
    • 18M30: string diagram, graphical calculi
    • 18M40: dagger category, categorical quantum mechanics
    • 18M50: rig category, lax monoidal category, duoidal category
    • 18M60: operad
    • 18M65: non-symmetric operad, multicategory, generalized multicategory
    • 18M70: algebraic operad, cooperad, Koszul duality
    • 18M75: topological operad, simplicial operad
    • 18M80: species, Hopf monoid, operad in combinatorics
    • 18M85: polycategory, dioperad, properad, PROP, cyclic operad, modular operad
    • 18M90: globular operad
  • 18Nxx: higher categories and homotopical algebra
    • 18N10: 2-category, bicategory, double category
    • 18N25: categorification
    • 18N30: strict $\omega$-category, computad, polygraph
    • 18N40: homotopical algebra, Quillen model category, derivator
    • 18N50: simplicial set, simplicial object
    • 18N65: (∞, n)-category, (∞, ∞)-category