The Publications of the nLab is a web-based journal for peer-reviewed publication of original research and expository writing on topics in mathematics and mathematical physics that are usefully discussed from the point of view of category theory and homotopy theory/higher category theory.

(For AuthorsFor RefereesFor Editors)


Published articles


The tools of category theory and higher category theory serve to organize other structures. There is a plethora of applications that have proven to be more transparent when employing the nPOV. Higher category theory has helped foster entire new fields of study that would have been difficult to conceive otherwise. The nLab is a place where researchers in this area are making notes about their field and their research, and writing up expositions, theorems, and proofs.

The goal of the Publications of the nLab is as a means to feed such content – as well as other submissions that wouldn’t otherwise find their way into the nLab – through peer-review to mark it explicitly as stable and reliable, and thus to make it citable.


The Publications of the nLab appear in the same wiki-format as the nLab in a way that facilitates thorough cross-hyperlinking. This allows nPublications-articles to conveniently refer their readers to background material on the nLab and allows nLab-articles to point their readers to stable and peer-reviewed results and proofs in the nPublications.

Contributions to the nPublications may vary in scope and form. The traditional article format submitted to printed journals is welcome, but the underlying wiki-technology may eventually find its own most natural form. The fact that background material can easily be linked to on the nLab opens the possibility to have peer-reviewed and published single theorems in the nPublications. At the other end of the spectrum, since there are hardly any size restrictions, whole books can find their place here. What counts is the quality and reliability of the content and its useful interlinking with other content.

Editorial board

At the moment the Publications of the nLab is in the developmental phase and a formal editorial board is yet to be set up. For the time being the nLab steering committee is the closest formal body responsible for the nPublications.

The preliminary list of tentatively confirmed names on an editorial board to be formally set up is

Submission procedure

An author who wishes to submit any material for publication to the Publications of the nLab should go through the following steps:

  1. Create the material to be submitted in separate pages on the nLab in the way any nLab pages are created (see nLab HowTo for details).

  2. Notify the editorial board of the nPublications about which pages in which precise version (as given in the edit-history of the entry) are to be submitted.

    (The precise version datum is mandatory for a submission to peer-review, as nLab entries are subject to potential perpetual edits.)

It is also possible to submit material for review in the form of a PDF document or arXiv entry, with the understanding that upon acceptance, conversion to nLab page(s) is a precondition for publication.

The submitted material will go through a refereeing process as usual in mathematical journals: specialist referees will be chosen by the editors. If the material is accepted, publication of the material proceeds as follows:

  1. The accepted version of the nLab entries is copied over to the write-protected nPublications web. (The nLab version of the submitted material remains in place, but is subject to perpetual further edits, as is all material on the nLab.)

  2. Hyperlinks are added (ideally by nPublications-staff, to the extent that such exists) to the nLab version of the submitted article, pointing to the stable peer-reviewed version published in the nPublications. Conversely, the nPublications-version is equipped with a link back to the freely editable nLab version.

Differences to traditional publication

Publication on a wiki-journal such as the Publications of the nLab is meant to retain the purpose and advantages of traditional journal publishing, which is

but add to it additional value that serves the scientific purpose.

Transparent refereeing

Traditional refereeing often degenerates to a formal procedure that serves the academic machinery more than the scientific purpose. On the nPublications we allow – if desired by referees – transparent refereeing that adds genuine scientific value to the process and its outcome. A single submitted article may receive one or more of the following stamps of approval.

Every article published in the Publications of the nLab carries an indication which kind of refereeing precisely it did receive. It may say:

  • This entry was refereed by n anonymous referees chosen and assumed to be expert by the editorial board.
  • The following people say that they read the entry and think that it is okay: name1, name2.
  • Contributior name3 started refereeing the article but ended up reworking it and adding to it substantially. The resulting new version can be found at the following link…

That link may point to an unrefereed nLab article, or again to the nPublications, where it may appear with its own list of people who looked at it.

As mentioned previously, due to its presentation in a wiki format, papers in the Publications of the nLab can make use of hyperlinks in a way which is not possible for papers published in a paper journal. Of course, references to other sections, theorems, definitions, and references can be linked, as is possible in PDF files using hypertex. But going beyond this, the material does not even have to be “projected in a totally ordered way onto the page axis” (in the immortal words of Serge Lang). It can be organized in a nonlinear way enabling readers to choose their own path through it more, “zooming in” by clicking on links to read more about those parts that interest them most.

Iterated resubmission

One advantage of a wiki such as the nLab over more static forms of presentation and publication is that it admits and encourages iterative improvement. No text is ever perfect and up-to-date, but on a wiki it can at least approach such a state asymptotically.

In order to have the write-protected Publications of the nLab take part in this perpetual improvement, iterated resubmissions are encouraged:

when the perpetual editing process of the nLab-version of an article published in the nPublications (by the original author or by other contributors) is recognized to have produced a significant improvement of the previous version (be it significant addition of new material or improvement of content or presentation of the original material), the original author or any other contributor is encouraged to resubmit a newer version of the page to the peer-review of the nPublications. It will be fed through the review process as usual, and if review is successful in that the new version is deemed by the referee(s) to be a genuine improvement on the former version, it replaces the former version on the nPublications. (Notice that no material on the wiki is ever deleted, all previous versions of any page are retained in the entry’s edit-history, accessible via a link at the bottom of every page.)

Publication of resubmissions are handled in a way that does not affect stability of citations. If a resubmission does not affect any previous citations to its content (for instance in the case that just an additional theorem is added) then it replaces the original page. If it does affect previous citations (for instance in the case that assumptions of theorems are being changed, maybe for fine-tuning the presentation) then the resubmission is published parallel to its earlier version.

Massively collaborative and third-party publishing

For science and for humanity, what counts is not the authorship of and fame and credit for a result. What counts is the result.

By its very nature, content on a wiki such as the nLab is potentially massively multi-authored and massively inter-linked with other pages to an extent that the resulting content may not be attributable to a single or even a handful of authors (even though every single edit is precisely attributable by the automatic edit history, the proverbial whole is typically more than the sum of these pieces). The result of this process is potentially of higher value than what any single contributing author could have achieved, and the nPublications is intended to make use of this.

Therefore the Publications of the nLab allows author-independent submission: if at any time a user of the nLab finds that any given version of any given nLab-page deserves formal peer-review, the user may submit that version to the nPublication as above.

The editorial board will decide if the submitted version indeed justifies feeding it through formal peer-review. It may suggest to the submitting user to wait with this until further improvements have been implemented.

Republication in other Journals

Publication in the Publications of the nLab does not preclude publication elsewhere. Initially, at least, we expect that publications in the Publications of the nLab will also be published elsewhere (either before or after their appearance in the nPublications ), and we rely on the authors to count them as only “one publication” on their CV with both places of publication listed. However, it will not be possible, in any case, to withdraw a paper once it has been published in the nPublications. The advantages to the author of also publishing in the Publications of the nLab include transparent refereeing, community input and potential branching, wide exposure, and availability of hypertext. Eventually, we hope that the Publications of the nLab will become respected enough that articles published there will be included into the main mathematics publications databases without the need for republication elsewhere.


The publisher of the Publications of the nLab is Andrew Stacey.

Revised on October 18, 2012 20:51:42 by Urs Schreiber