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} 31546
18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory 18
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 1187
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 1859
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 717
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} 1086
18D25 Actions of a monoidal category, tensorial strength {For functional programming, see also 68N18} 60
18D40 Internal categories and groupoids {For double categories, see 18N10; for topological groupoids, see 22A22; for Lie groupoids, see 58H05} 13
18E13 Protomodular categories, semi-abelian categories, Mal’tsev categories [See also 08B05 and 08B10] 50
18E35 Localization of categories, calculus of fractions {For homotopical aspects, see also 18N55, 55P60} 454
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) [See also 14F06, 14F08, 32C35, 32L10, 54B40, 55N30] 1255
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] 1841
18Gxx Homological algebra in category theory, derived categories and functors [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx] 7202
18G05 Projectives and injectives (category-theoretic aspects) [See also 13C10, 13C11, 16D40, 16D50] 585
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) [See also 55U25] 745
18G70 \(A_{\infty}\)-categories, relations with homological mirror symmetry [See also 14F08, 14J33, 53D37] 26
18G90 Other (co)homology theories (category-theoretic aspects) [See also 19D55, 46L80, 58J20, 58J22] 55
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} 156
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} 159
18N55 Localizations (e.g., simplicial localization, Bousfield localization) [See also 18E35, 55P60] 28
18N60 \((\infty,1)\)-categories (quasi-categories, Segal spaces, etc.); \(\infty\)-topoi, stable \(\infty\)-categories [See also 55U35, 55U40] 85