Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  1. Page created, but author did not leave any comments.

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 18th 2021

    Question on whether this terminology is used in the literature. Also, an alternative definition via enrichment in pointed sets.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorHurkyl
    • CommentTimeJun 18th 2021
    • (edited Jun 18th 2021)

    I assume “wedge product” did not mean to link to “exterior algebra”, so I changed it to “smash product”.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2021
    • (edited Jun 18th 2021)

    rather: smash product [ edit, ah, I see you changed it ]

  2. Original author here: this article was created because I was making articles for oidifications of various algebraic structures (i.e. differential algebroid for differential algebra); I seemed to have forgotten to put in an ideas section when writing this article; this should be the oidification of an absorption monoid.

    Anonymous

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 18th 2021

    Is the terminology “absorption category” something that occurs in the literature?

    (Maybe the same type of terminological question could be asked of many articles in this proliferation of oidification articles.)

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeJun 18th 2021
    To be honest, most likely no, but Urs Schreiber did not seem to have an issue with these articles when they were first created.
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 19th 2021

    There is decidedly no requirement for nnLab contributions (including concepts and notation) to be confined to what already occurs in the literature. On the contrary, where this is the case it tends to serve as background material for other contributions that the author cares to record here precisely because they are not yet in the literature, or not in a given form or from a given perspective. This explicit contrast to other places, like Wikipedia or also the StacksProject (I suppose) etc. got enshrined in the pun of the nPOV.

    This policy makes contributing to and reading of the nnLab potentially more interesting but also potentially more risky than at other places, because it means that material that appears may not have been vetted and not have been “peer reviewed”, certainly not the moment it is becomes visible on published nnLab pages.

    Another crucial aspect of the nnLab is that there is in practice no bounds on resources. As long as contributions are sane and of potential use to at least the author themselves, there is no harm having them.

    In the present case, my understanding is that our “Guest” set themselves the goal of making explicit the oidification of a whole list of common basic notions of algebra, and, for completeness, to introduce/invent the (mostly evident) terminology where not yet established.

    I think that’s clearly sane, plausibly of potential interest to various readers even if not to others (as it goes) and in fact potentially a good basis for establishing a lot of cross-links between existing and not-yet existing entries.

    There is an evident question of design decision: Given that most of these oidifications are straightforward and done justice by just a few lines of text, one might have decided to keep them all in a list on a single nnLab page. On the other hand, as soon as anyone actually does want to explicitly refer to any item in this list, it is much more convenient for both author and their readers if that item has its own entry. And since, as above, there is no practical constraint on the number of entries, it doesn’t seem to hurt to have lots of little entries.

    In conclusion, I see no reason to discourage our “Guest” from what they are doing. What I would do is ask to keep in mind to make clear to the reader in each and every Idea-section what kind of material it is they are being confronted with: If an entry introduces new terminology, then this is fine, but should be made crystal clear to the reader right up-front. Similarly for the purpose of the entry: If there is risk that readers might be puzzled as to what point an entry has, then it should be made clear right there in the Idea-section.

    In the present case this might mean that the Idea sections should generally amplify/recall (a) the concept of oidification aka horizontal categorification and (b) the fact that there are many basic notions in algebra whose horizontal categorification either has not been considered at all, or has been considered, but under an unrelated name. And the point of all these entries is make this secret systematics of horizontal categorification more broadly explicit.

    Quite in line with the nPOV, even if for “horizontal nn”, here.

    • CommentRowNumber9.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 19th 2021

    That seems very reasonable, Urs.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)