16B50 Category-theoretic methods and results in associative algebras (except as in 16D90) [See also 18-XX] 553
18-XX Category theory; homological algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} 28790
18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory 18
18-03 History of category theory [Consider also classification numbers pertaining to Section 01-XX] 84
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 1095
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 1788
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 636
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads [See also 18Gxx] {For functional programming, see also 68N18} 981
18D25 Actions of a monoidal category, tensorial strength {For functional programming, see also 68N18} 51
18D40 Internal categories and groupoids {For double categories, see 18N10; for topological groupoids, see 22A22; for Lie groupoids, see 58H05} 4
18E13 Protomodular categories, semi-abelian categories, Mal’tsev categories [See also 08B05 and 08B10] 7
18E35 Localization of categories, calculus of fractions {For homotopical aspects, see also 18N45, 55P60} 412
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) [See also 14F06, 14F08, 32C35, 32L10, 54B40, 55N30] 1155
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 1807
18Gxx Homological algebra in category theory, derived categories and functors [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx] 6398
18G05 Projectives and injectives (category-theoretic aspects) [See also 13C10, 13C11, 16D40, 16D50] 546
18G15 Ext and Tor, generalizations, KĂĽnneth formula (category-theoretic aspects) [See also 55U25] 710
18G70 \(A_{\infty}\)-categories, relations with homological mirror symmetry [See also 14F08, 14J33, 53D37] 12
18G90 Other (co)homology theories (category-theoretic aspects) [See also 19D55, 46L80, 58J20, 58J22] 17
18M15 Braided monoidal categories and ribbon categories {For applications to knot theory, see also 57Kxx; for applications to quantum groups, see also 16T20, 17B37, 81R50} 45
18M20 Fusion categories, modular tensor categories, modular functors {For applications to topological quantum field theories, see also 57R56; for applications to conformal field theories, see also 81T40} 43
18N55 Localizations (e.g., simplicial localization, Bousfield localization) [See also 18E35, 55P60] 4
18N60 \((\infty,1)\)-categories (quasi-categories, Segal spaces, etc.); \(\infty\)-topoi, stable \(\infty\)-categories [See also 55U35, 55U40] 31
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} 127189
46M15 Categories, functors in functional analysis {For \(K\)-theory, Ext, etc., see 19K33, 46L80, 46M18, 46M20} 543
46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 272
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) [See also 14F06, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx] 1302