Dear all, the Mathematics Subject Classification will soon be revised by Mathematical Reviews and Zentralblatt, aiming at a new edition, MSC2020. They are soliciting suggestions and feedback until August 8th. Three of us (Emily Riehl, Steve Lack, Joachim Kock) have been collaborating on a proposal for Section 18 (Category theory; homological algebra). The main point of the proposal is to create new subsections 18H Higher categories and homotopical algebra 18M Monoidal categories and operads, big subfields of category theory where it is particularly difficult to find good entries in the MSC2010. We also take the opportunity to propose some adjustments in the existing subsections of 18. The proposed new Section 18 is included below in plain text. A more detailed document, with change comments, can be accessed at this link: https://www.dropbox.com/s/yr400e893uhhctm/MSC2020.pdf?dl=0 We are still fine-tuning the proposal. Before submitting the proposal (one week from now), we would like to request last-minute feedback from the category theory community, either on this mailing list or in private. We also invite you to co-sign the proposal. We are sorry for getting this proposal out so late. But this is only the starting point: the next phase in the timeline set out by MR and zbMATH is 12 months of community feedback, so there will still be plenty of time for discussion. Best wishes, Emily Riehl, Joachim Kock, Steve Lack. ---- 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 18-01 Instructional exposition (textbooks, tutorial papers, etc.) 18-02 Research exposition (monographs, survey articles) 18-03 Historical (must also be assigned at least one classification number from Section 01) 18-04 Explicit machine computation and programs (not the theory of computation or programming) 18-06 Proceedings, conferences, collections, etc. 18Axx General theory of categories and functors 18A05 Definitions, generalizations 18A10 Graphs, diagram schemes, precategories 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 systems, substructures, quotient structures, congruences, amalgams 18A35 Categories admitting limits (complete categories), functors pre- serving limits, completions 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18A99 None of the above, but in this section 18Bxx Special categories 18B05 Categories of sets, characterizations [See also 03-XX] 18B10 Categories of relations, spans, or partial maps 18B15 Embedding theorems, universal categories [See also 18E20] 18B20 Categories of machines, automata [See also 03D05, 68Qxx] 18B25 Toposes [See also 03G30, 18F10] 18B30 Extensive, distributive, and adhesive categories 18B35 Preorders, orders, domains, and lattices (viewed as categories) [See also 06-XX] 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 18B99 None of the above, but in this section 18Cxx Categories and theories 18C05 Equational categories [See also 03C05, 08C05] 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also 03G30] 18C15 Monads (= standard construction or triple), algebras for a monad, homology and derived functors for monads [See also 18Gxx] 18C20 Eilenberg-Moore and Kleisli constructions for monads 18C30 Sketches and generalizations 18C35 Accessible and locally presentable categories 18C40 Structured objects in a category (group objects, etc.) 18C50 Categorical semantics of formal languages [See also 68Q55, 68Q65] 18C99 None of the above, but in this section 18Dxx Categorical structures 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) 18D20 Enriched categories (over closed or monoidal categories) 18D25 Strong functors, strong adjunctions 18D30 Fibered categories 18D35 Structured objects in a category (group objects, etc.) 18D40 Internal categories 18D60 Profunctors (=correspondences, distributors, modules) 18D65 Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads) 18D70 Formal category theory 18D99 None of the above, but in this section 18Exx Categorical algebra 18E05 Preadditive, additive categories 18E08 Regular categories, Barr-exact categories 18E10 Abelian categories 18E13 Protomodular categories, semi-abelian categories, Mal???tsev cate- gories 18E15 Grothendieck categories 18E20 Embedding theorems [See also 18B15] 18E35 Localization of categories, calculus of fractions [for homotopical aspects, see also 18H45, 55P60] 18E40 Torsion theories, radicals [See also 13D30, 16S90] 18E45 Definable subcategories and connections with model theory [See also 13C60] 18E50 Categorical Galois theory 18E99 None of the above, but in this section 18Fxx Categories in geometry and topology 18F05 Local categories and functors 18F10 Grothendieck topologies and Grothendieck toposes [See also 14F20, 18B25] 18F15 Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx] 18F20 Presheaves and sheaves, stacks, descent conditions [See also 14F05, 32C35, 32L10, 54B40, 55N30] 18F25 Algebraic K-theory and L-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 18F30 Grothendieck groups [See also 13D15, 16E20, 19Axx] 18F40 Synthetic differential geometry, tangent categories, differential categories 18F50 Goodwillie calculus and manifold calculus 18F60 Categories of topological spaces and continuous mappings 18F70 Frames and locales, pointfree topology, Stone duality 18F99 None of the above, but in this section 18Gxx Homological algebra and derived categories [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx] 18G05 Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50] 18G10 Resolutions; derived functors [See also 13D02, 16E05, 18E25] 18G15 Ext and Tor, generalizations, K??nneth formula [See also 55U25] 18G20 Homological dimension [See also 13D05, 16E10] 18G25 Relative homological algebra, projective classes 18G30 Simplicial modules and Dold???Kan correspondence 18G35 Chain complexes and dg-categories [See also 18G60, 55U15] 18G40 Spectral sequences, hypercohomology [See also 55Txx] 18G45 2-groups, crossed modules, crossed complexes 18G50 Nonabelian homological algebra 18G60 Derived categories, triangulated categories 18G65 Stable module categories [see also 20C20] 18G70 A???-categories, relations with homological mirror symmetry 18G80 Categorification (e.g. of quantum groups and graph polynomials) [See also 18M25, 17B37, 20G42, 05C31] 18G85 Graph complexes and graph homology [for relations with deformation quantization, see 53D55] 18G90 Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22] 18G99 None of the above, but in this section 18Hxx Higher categories and homotopical algebra 18H10 2-categories, bicategories, double categories 18H15 2-dimensional monad theory [See also 18C15] 18H20 Tricategories, weak n-categories, coherence, semi- strictification 18H30 Strict omega-categories, computads/polygraphs, applications to term rewriting 18H40 Homotopical algebra. Quillen model categories, derivators 18H45 Categories of fibrations, relations to K-theory, relations to type theory 18H50 Simplicial sets, simplicial objects in categories and ???-categories, simplicial sheaves [See also 55U10] 18H55 Localizations (e.g. simplicial localization, Bousfield localization) [See also 18E35, 55P60] 18H60 (???, 1)-categories (quasi-categories, complete Segal spaces, etc.); ???-topoi, stable ???-categories [See also 55U35, 55U40] 18H65 (???, n)-categories and (???, ???)-categories 18H70 ???-operads and higher algebra [See also 18M75] 18H99 None of the above, but in this section 18Mxx Monoidal categories and operads 18M05 Monoidal categories, symmetric monoidal categories [See also 19D23] 18M10 Traced monoidal categories, compact closed categories, star-autonomous categories 18M15 Braided monoidal categories and ribbon categories {For applications to knot theory, see also 57M25; for applications to quantum groups, see also 16T20, 17B37, 81R50} 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} 18M25 Tannakian categories {For applications to motives, see also 14C15, 19E15} 18M30 String diagrams and graphical calculi 18M35 Categories of networks and processes, compositionality 18M40 Dagger categories, categorical quantum mechanics 18M45 Categorical aspects of linear logic [See also 03B47] 18M50 Quantales [see also 06F07 and 18B35] 18M55 Bimonoidal, skew monoidal, duoidal categories 18M60 Operads 18M65 Non-symmetric operads, multicategories, generalized multicategories 18M70 Algebraic operads, cooperads, and Koszul duality 18M75 Topological and simplicial operads [see also 18H60] 18M80 Species, Hopf monoids, operads in combinatorics 18M85 Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads 18M90 Globular operads 18M99 None of the above, but in this section ---- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]