The nLab is a collaborative wiki. It grew out of the desire (I, II) to have a place for development (the “Lab” in “$n$Lab”) and indexed archives of the ideas and concepts surrounding the discussions at the The $n$-Category Café. These discussions primarily are about mathematics, physics and philosophy from the higher structures point of view of homotopy theory/algebraic topology, homotopy type theory, higher category theory and higher categorical algebra (the “$n$” in “$n$Lab” and “nPOV”), as well as from the perspective of string theory for physics related articles.
The $n$Lab was created in November 2008 by Urs Schreiber, using software provided and set up by Jacques Distler. The name “$n$Lab” (short for “$n$-Category Lab”, but perhaps less restrictive) was dreamt up by Lisa Raphals (John Baez‘s wife).
Discussion of and around edits to the $n$Lab happen on the $n$Forum which roughly plays the role of the “talk”-pages at Wikipedia.
The most apt analogy for the $n$Lab is of a group lab book. A lab book for a research scientist is a place where they write down anything that they consider relevant for their work; a group lab book is one that several researchers with common interests use. The material recorded in a lab book can include:
Apart from not having actual physical experiments, this matches the content of the $n$Lab fairly well. The key difference between the $n$Lab and an “ordinary” lab book is that it is public. By making it public we hope to achieve two things:
There is much more to a research project than that which appears in the final paper and we believe that since our results and our final proofs will be public, then both we and those who might read such a paper can benefit from beginning the interaction much earlier in its development.
Thus by making our lab book public, we hope that casual passers-by will stop, read, and scribble something on it that will help us do our research.
There are three things to say about this that are worth making very clear.
For more recent impressions of the nature of this wiki see also at: What is… the nLab.
The $n$Lab is not a community project set up for the education and improvement of Humanity. It originally grew out of the The $n$-Category Café and the loose-knit community surrounding that blog. It is not possible to give a precise description of who is in that community, and the community involved in the $n$Lab has itself evolved from that starting point. Moreover, even if it were possible to describe that community we would not wish to. We are not a closed group, we are always keen for others to join us. The two simple rules are:
The way that this is being worked out in practice is as follows. Currently it seems that common motivations for contributing to the $n$Lab are
to assemble information on mathematics, physics and philosophy in a modern unified way, from the perspective of higher algebra, homotopy theory, type theory, category theory, and higher category theory, as well as from the perspective of string theory for physics related articles
to provide exposition of this information which is useful to a wide range of readers of differing expertise;
to jointly develop ideas and research on applying higher algebraic, homotopical, type theoretic, categorical, and higher categorical concepts and tools to issues in mathematics, physics and philosophy, and string theory concepts and tools to issues in physics.
To some extent this involves
But on top of this encyclopaedic function, and hopefully in parallel to that, the $n$Lab is
These points together imply that
on the $n$Lab we do not hesitate to provide non-traditional perspectives, definitions and explanations of terms and phenomena for mathematics, physics, and philosophy, if we feel that these are the right perspectives, definitions and explanations from a modern unified higher algebraic, homotopical, type theoretic, categorical, and higher categorical perspective, and we also do not hesitate to provide non-traditional perspectives, definitions and explanations of terms and phenomena for physics if we feel that these are the right perspectives, definitions and explanations from a string theory perspective;
at the same time we want to indicate clearly which part of an entry is traditional common material, which is a modern but widely-accepted reformulation and which is genuinely the result of original research by a contributor or by several contributors;
we will intersperse possibly controversial but always constructive discussion into entries if we feel the need. While in general the nforum is where we have chat and discussion and the $n$Lab is where we compile material, few entries on the $n$Lab are or can be meant as representing a final truth. The $n$Lab will be the better the more we discuss its contents. For more on how to inject discussion into entries see the HowTo page.
Most importantly the $n$Lab is
If you find yourself annoyed by the state any given entry is in, for whatever reason, please feel encouraged to edit it in order to improve the situation.
Notice: an entry being in a pitiful state is usually more a sign of nobody having spared the time and energy to work on it, than of our joint incompetence to write a decent entry if we were being paid for doing it. So if you find your eyebrows raised by some entry, don’t turn away to be the next one not to work on it. Instead, improve it. We all do this voluntarily. Most of us have other duties to attend. So don’t be annoyed with “us”, help us.
So if you feel existing material needs to be changed, you can do so. If you feel further material needs to be added, different perspectives need to be amplified, you can add a new paragraph, headed by a suitable headline. Be bold: The $n$Lab will be the better the more people decide to contribute to it.
See the HowTo page for information on how to contribute to the $n$Lab and edit and/or create its entries.
Historically, the nlab was powered by Instiki, but now runs on a custom fork. All 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 at github.
The physical server running the nLab lives at Carnegie Mellon University, and is supported by the homotopy type theory MURI award FA9550-15-1-0053 from the United States 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.
Last revised on January 21, 2023 at 08:20:29. See the history of this page for a list of all contributions to it.