Re: MSC2020, Section 18

Re: MSC2020, Section 18

[Marta Bunge]

Dear Joachim,


After perusing the proposed changes, I offer some possible additions, which  I list for your consideration.



18C15.  Add "Distributions and Distribution Algebras"


18D25.  Add  "Lax Functors, Lax Adjointness"


18D30.  Add "Complete Spreads over Generalized Spaces"


18E50.  Add "Fundamental Groupoids for Generalized Spaces"


18F40.  Add or Insert "Synthetic Differential Topology".



I can add some justifications if need be.


Best regards,

Marta

________________________________
From: Joachim Kock <kock@mat.uab.cat>
Sent: August 1, 2018 8:32:50 AM
To: categories@mta.ca
Subject: categories: MSC2020, Section 18

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.



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: MSC2020, Section 18

[Joachim Kock]

Hi again,

the proposal has now been submitted to MSC2020.org.
The final version of the proposal can be found here:

https://www.dropbox.com/s/xu91w2josvuua24/MSC2020-Section18.pdf

(It is not very different from last week's version.)

Cheers,
Joachim.


On 01/08/2018 22:32, Joachim Kock wrote:
> 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.


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

MSC2020, Section 18

[Joachim Kock]

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

----


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