physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics


Search the nLab (hints)


This is a wiki for collaborative work on Mathematics, Physics and Philosophy — especially, but far from exclusively, from the n-point of view: with a sympathy towards the tools and perspective of category theory and higher category theory.



The nLab records and explores a wide range of mathematics, physics, and philosophy. Along with work of an expository nature, original material can be found in abundance, as can notes from evolving research.

If you take a little time to find something in the literature, or to work through a proof or example, or to find an intuitive or new way to think about something, add a note on it to the nLab! Others will benefit, and you may well find that it proves useful to you too.

A fundamental idea behind the nLab is that the linking between pages of a wiki is a profound way to record knowledge, placing it in a rich context.

For more, see Urs Schreiber’s thoughts at What is… the nLab?. Further details can be found at About.

Discussion, Comments, Questions

While we work on the nnLab, we talk to each other on the nForum. In particular, for all but the most trivial edits (correcting spelling or punctuation, etc.), we make a note of our latest edits to the nnLab in the part nForum – latest changes, where they may be discussed further.

If you do make contributions to the nnLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum for more information.

If you do not want to contribute to the nnLab, but if you have comments on an entry – say because you are an expert and feel that information is wrong or missing – or questions – say because you are a layperson and feel that things could be explained better – then we generally prefer that you post that comment or question to the nForum, where it is visible to everybody who might be concerned.

In case that you do feel that this is not an option and that you do need to contact privately (say by email) a single author of an nnLab page, please make sure that you know who the right author is. Beware that the nnLab pages are visibly “signed” only by the name of the last person who made any edit on the page, no matter how minor. To find the author who made the edit that you want to comment or ask about privately, you should click on the link “History” at the bottom of any page to see which version was authored by whom.

Contributing to the nnLab

If after looking around for a while you feel like contributing yourself, you are welcome to do so. But read About to be sure you understand what we are doing here (to the extent that we understand this ourselves, at least). If you feel unsure about appropriate content, see What to Contribute. For technical hints see HowTo.

If you make any edits to the nnLab, please inform the rest of the nnLab community by dropping a brief message in the latest changes section of the nForum!

Using the nnLab

One goal of the nnLab is to help make information widely available and usefully related to other information. In this users and contributors are expected to follow traditional academic practice:

  • Using and distributing content obtained from the nnLab is free and encouraged if you acknowledge the source, as usual in academia.

    (There is currently no consensus on a more formal license statement, but if it matters check if relevant individual contributors state such on their nnLab homepages.)

    If you cite a page you may want to point to a specific version of it, because nnLab pages can change. You can find a list of all the versions of a page by clicking on the History link at the bottom of the page itself.

  • Conversely, any content contributed to the nnLab is publicly available and you should be aware that others may use your contributions (whatever you decide to do with their content elsewhere) and indeed may edit them. In the first case you trust that users will cite your contributions properly, in the second that they will respect and only improve on them. At the same time, you are expected to properly acknowledge sources of information for material entered into the nnLab.

Usually this works well. If there is need for discussion, the nForum is the forum to turn to. If serious problems arise, the steering committee might intervene.

Software requirements

The nnLab sends mathematical formulas to the browser using MathML.

Notice that you don’t need to know any MathML for editing the nnLab, only your browser does. You write formulas into the nnLab between dollar signs in iTeX, which is very similar to ordinary LaTeX.

Presently only Firefox and its derivatives have implemented native rendering of MathML. Presently all other browsers fall back to invoking MathJax. This works fine on small pages, but on pages with substantial content the MathJax rendering takes up to several minutes.

This means that presently you should use Firefox or its derivatives to view the nnLab (free download of Firefox).

Server and setup

The domain is owned by Urs Schreiber.

The nnLab server is currently hosted at Carnegie Mellon University, funded in the context of the HoTT MURI grant.

The nLab runs on a server at Carnegie Mellon University that is supported by MURI grant FA9550-15-1-0053 from the Air Force Office of Scientific Research. Any opinions, findings and conclusions or recommendations expressed on the nLab are those of the authors and do not necessarily reflect the views of the AFOSR.

However, we will imminently be moving to the cloud, to an account registered to the Topos Institute. We are currently raising funds; please contribute if you can!

The development of the nLab software and technical administrative matters are currently in the hands of Richard Williamson and assistant Alexis Hazell. If you wish to lend a hand, please contact us.

Much of the software behind the nLab has been written especially for the nLab: the latest source can be found at GitHub. It was originally an instance of Instiki, and the shell of it remains (for the moment). Bug reports or other software issues/requests for the nLab are currently best raised in the category nLab Technical Matters at the nForum, but can also be posted on GitHub.

The nnLab page style is due to Jake Bian, originating with his Kan browser extension

The nnLab logo is due to David Roberts, inspired by Matisse’s painting La Gerbe. Besides being an inside reference to higher structures known as gerbes, the logo represents maybe computational trinitarianism or the progression of modalities or generally the unity of diverse mathematical phenomena revealed by the nPOV.

Steering Committee

The nnLab is a community undertaking. But for all matters that do require that the nnLab is represented to the outside by an official decision-taking body, we have the steering committee. Nobody “is in charge of the nnLab”. But the steering committee is the closest approximation to a body being in charge that we have.

category: meta

Last revised on February 28, 2021 at 17:49:04. See the history of this page for a list of all contributions to it.