The n-Category Café

The project originated from a set of ~10500 pages of PDF notes, as discussed a bit in the Progress page. These are being gradually polished, revised, expanded, and converted into Gerby’s web format.

A large chunk of the material so far consists of “housekeeping” for what is yet to come. For instance, there’s lots of elementary material on relations, intended to later serve as a stepping stone for the chapter(s) on profunctors, as well as examples for notions in 2-category theory like internal monads. The material is first and foremost developed from a category-theoretical point of view, something that is perhaps made particularly clear by Tag 00KV.

However, over the course of the coming months/years, I’m hoping to expand, revise, convert, and develop the foundational category theory material in the web version of Clowder. Eventually, I plan to also cover more “advanced” subjects like category theory variants (fibred, enriched, internal), as well as higher category theory (bicategories, double categories, etc.).

I’ve recently pushed a significant update on July 06 fixing a number of bugs that had been plaguing Clowder since it went up. Along the way, I’ve also implemented (or finished implementing) a number of useful new features and additions that aren’t present in the Stacks Project/Kerodon, including:

1. Documentation on how to build Clowder from source as well as a set of GitHub actions that automatically do it whenever a new update comes out, building the latest version via GitHub Pages.
2. A dark mode.
3. A preferences dialogue where you can select different fonts for the web version and the PDFs.
4. A better view for math environment tags like definitions or propositions, which are rendered inside each subsection, but with the rest of the subsection content blurred (example).
5. Copyable code and syntax highlighting for bibliography entries (example).

Comments are very welcome!

Some general information/notes:

1. The project has a different set of goals than the nLab, as explained in Tag 02CC.
2. The general nature and goals of the project are discussed in Tag 01WM in particular, and in “Chapter 1: Introduction” in general.
3. Tag 01X3 contains a collection of nice results and general things from Clowder.
4. There will be material on ∞-categories, but in a different way than Kerodon, so Clowder should eventually form a good complement to it.
5. The project has an associated Discord server for updates, discussions, etc.