suggestions for the 2020 MSC classifications

suggestions for the 2020 MSC classifications

[Emily Riehl]

Hi all,

I’ve recently learned that Zentralblatt and the Mathematics Reviews are collaborating to revise the Mathematics Subject Classifications (MSC) for 2020. The current MSC2010 codes were a revision of the original MSC2000 codes. You can read more about this here:

https://blogs.ams.org/beyondreviews/2016/07/26/msc2020-mathematics-subject-classification-update/ <https://blogs.ams.org/beyondreviews/2016/07/26/msc2020-mathematics-subject-classification-update/>

The editors of zbMath and MR are inviting suggestions from the community as part of this process and I think category theory should weigh in about the 3- and 5-digit subject classifications housed under “18.” This might not be the most important thing in the world but on the other hand, I could imagine working as a mathematician whose primary research area is (say) 55 or 3, searching for MSC codes to add to a paper before uploading to the arXiv, finding a particularly apt one under 18, and then gradually over many years of this starting to think of myself as a category theorist, in part, too. 

I’d rather not be the one to curate feedback regarding the MSC codes but if no other volunteer presents themselves, I’ll at least send an email summarizing the discussion that takes place here. 

I’m appending some emails that came over the homotopy type theory list (which is how I first learned about the classification update) as an illustration of the kind of discussion that I hope we’ll have in category theory.

Best,
Emily
—
Assistant Professor, Dept. of Mathematics
Johns Hopkins University
www.math.jhu.edu/~eriehl <http://www.math.jhu.edu/~eriehl>

> From: Ulrik Buchholtz <ulrikbuchholtz@gmail.com <mailto:ulrikbuchholtz@gmail.com>>
> Subject: [HoTT] HoTT/UF in MSC2020
> Date: January 11, 2018 at 6:45:12 AM GMT+11
> To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com <mailto:HomotopyTypeTheory@googlegroups.com>>
> 
> MR (Mathematical Reviews) and zbMATH are currently soliciting comments for the upcoming MSC (Mathematics Subject Classification) 2020 at https://msc2020.org/ <https://msc2020.org/>
> 
> I would like to suggest some new entries for the work that we do, as it is not always a perfect fit for the old MSC 2010 system. (To put it mildly!)
> 
> But what should we suggest? This wasn't entirely clear to me either, and I was hoping that we could have a discussion about that here, and then submit our consensus proposal (if we can get one) at msc2020.org <http://msc2020.org/>.
> 
> To get started, what do you think of the following:
> 
> Under 03B General Logic, we add: 03B16 Dependent type theory (in general) [or Martin-Löf type theory], and 03B17 Homotopy type theories (Dependent type theories from a homotopical point of view)
> 
> Under 03F Proof theory and constructive mathematics, we add: 03F57 Univalent mathematics
> 
> [With cross references.]
> 
> But what about 18 Category Theory and 55 Algebraic Topology? Infinity-topos theory and the relations to HoTT/UF don't really fit in the existing categories there, either.
> 
> Looking forward to your comments,
> Ulrik

> From: Michael Shulman <shulman@sandiego.edu <mailto:shulman@sandiego.edu>>
> Subject: Re: [HoTT] HoTT/UF in MSC2020
> Date: January 11, 2018 at 9:00:03 PM GMT+11
> Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com <mailto:HomotopyTypeTheory@googlegroups.com>>
> 
> 
> I agree with proposing adding "dependent type theories" to 03B,
> although one could argue that it fits under 03B15 "Higher-order logic
> and type theory".
> 
> I don't think I would put homotopy type theories in 03B, though; it
> seems too specific.  Syntactic study of homotopy type theories could
> go under your 03B16, while semantic study could go under 18C50
> "Categorical semantics of formal languages" and/or 03G30 "Categorical
> logic, topoi".  For higher categories/toposes themselves there are
> 18D05 "Double categories, $2$-categories, bicategories and
> generalizations" (although that should be renamed to something like
> "higher categories", and maybe moved to somewhere other than 18D
> "Categories with structure") and 18B25 "Topoi" (which I would
> interpret to include higher topoi as well -- although I don't
> understand why 18B25 is under 18B "Special categories").
> 
> I might propose replacing 55U35 "Abstract and axiomatic homotopy
> theory" and 55U40 "Topological categories, foundations of homotopy
> theory" with three topics like "Model categories and generalizations",
> "Homotopy theory in higher categories (see also 18D05)", and
> "Synthetic homotopy theory (see also 03B16, 18C50, 03G30)".
> 
> What seems to me like the really egregious mistake is lumping together
> "Proof theory and constructive mathematics" in 03F, since most
> constructive mathematics has nothing to do with proof theory.  What
> about proposing a new three-digit [sic] classification like "03I
> Mathematics done using alternative foundations", which could contain
> things like 03I01 "Constructive mathematics" and 03I02 "Univalent
> mathematics" -- distinguishing the *use* of such foundations from
> their *metatheoretic* study (which is what most 03 "Mathematical logic
> and foundations" seems to be about).
> 
> Overall, it's unclear to me what the criteria should be for giving a
> subject its own three- or five-digit classification.  The community of
> univalent mathematics and synthetic homotopy theory is still quite
> small relative to all of mathematics, so we might not be justified in
> asking for our own five-digit classification(s).  On the other hand,
> many of the existing five-digit classifications seem to me, as an
> outsider of the fields in question, to be *extremely* narrow.  It
> would be useful to have some data regarding how much mathematics is
> being done under existing classifications; are there existing
> five-digit subjects whose communities are the same size as HoTT/UF or
> smaller?  Is there any good way to get (or approximate) such data?


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Re: suggestions for the 2020 MSC classifications

[John Baez]

Hi -

I often find it awkward choosing Mathematics Subject Classifications
for papers on category theory.  One can imagine elaborate schemes, but
mainly I'd like a number for "higher categorical structures" (to cover
everything on 2-categories, n-categories, n-tuple categories etc.).
It would also be nice to have one for "topos theory".

I'd be happy to get rid of this:

18D25   Strong functors, strong adjunctions

I'm afraid I don't even know what these are!

Best,
jb


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Re: suggestions for the 2020 MSC classifications

[Steve Awodey]

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Dear Emily,

> On Feb 25, 2018, at 7:45 PM, Emily Riehl <eriehl@math.jhu.edu> wrote:
> 
> Hi all,
> 
> I’ve recently learned that Zentralblatt and the Mathematics Reviews are collaborating to revise the Mathematics Subject Classifications (MSC) for 2020. The current MSC2010 codes were a revision of the original MSC2000 codes. You can read more about this here:
> 
> https://blogs.ams.org/beyondreviews/2016/07/26/msc2020-mathematics-subject-classification-update/ <https://blogs.ams.org/beyondreviews/2016/07/26/msc2020-mathematics-subject-classification-update/>
> 
> The editors of zbMath and MR are inviting suggestions from the community as part of this process and I think category theory should weigh in about the 3- and 5-digit subject classifications housed under “18.” This might not be the most important thing in the world but on the other hand, I could imagine working as a mathematician whose primary research area is (say) 55 or 3, searching for MSC codes to add to a paper before uploading to the arXiv, finding a particularly apt one under 18, and then gradually over many years of this starting to think of myself as a category theorist, in part, too. 
> 
> I’d rather not be the one to curate feedback regarding the MSC codes but if no other volunteer presents themselves, I’ll at least send an email summarizing the discussion that takes place here. 

thanks for volunteering ; - )

it seems to me that there needs to be a section 18Hxx for Higher Categories, under which all higher-dimensionl CT falls, classified by appropriate subsections like: 
2- and Bicategories, Quasi-Categories, Strict n-categories, Double Categories, etc. 

Steve



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