- locally finitely presentable

- Barr-exact (aka effective regular)

but is not the category of algebras of a Lawvere algebraic theory? ]]>

There’s some discussion on the page (towards the end of this section) that needs to be removed when we can.

]]>And while I am at it, some general background references:

Jürgen Tappe,

*Irreducible projective representations of finite groups*, Manuscripta Math 22, 33–45 (1977) (doi:10.1007/BF01182065)Tania-Luminiţa Costache,

*On irreducible projective representations of finite groups*, Surveys in Mathematics and its Applications**4**(2009), 191-214 (ISSN:1842-6298)Eduardo Monteiro Mendonça,

*Projective representations of groups*, 2017 (pdf)

Sorry, I was just confused. It all makes sense.

]]>The formula in question shows the operation in an abelian group object in the slice of $CRing$ over $R$. On the left we have an element in the fiber product over $R$, which is why the variable $r$ appears duplicated. This was probably meant to make it clearer (the text around it seems pretty explicit), though I can see that it can be confusing: But the fiber product object on the left is thus the ring $R \oplus N \oplus N$.

]]>For when editing functionality is back:

While fairly straightforward, it’s useful to make explicit that character theory by and large still works for projective representations:

- Chuangxun Cheng,
*A character theory for projective representations of finite groups*, Linear Algebra and its Applications**469**(2015) 230-242 (doi:10.1016/j.laa.2014.11.027)

Internet archive is an option, people are doing that more at MO.

]]>John, I don’t think the article is alleging that this is the ring multiplication on the square-zero extension. There’s some more information at Beck module.

]]>In the page Kähler differential the second displayed equation is a formula for multiplication in $R \oplus N$ where $R$ is a commutative ring and $N$ is an $R$-module. This formula looks wrong because the variable $r$ appears twice at left when we should be multiplying two different elements of $R \oplus N$; also it does not use the $R$-module structure of $N$. What’s the intended formula? (I can guess one but…)

]]>Thanks for this heads-up.

Link rot is a real issue for our pages. In the case of author pdf-files that are not stably hosted elsewhere (such as PhD theses that are kept only on the author’s website) I have adopted the habit of saving a local copy to the nLab server and linking that in addition to the author’s original. For videos this practice is maybe neither practical nor reasonable (and in fact impossible under the existing file size constraints, though this could change, now that Richard is reworking the whole installation).

]]>One minor issue:

It used to be the case that, when following a link to an anchor inside a page, the target paragraph would be highlighted by a gray background box.

(We had introduced this years back when we found that, otherwise, it can be hard for the reader to figure out where exactly they are being pointed to. This is particularly relevant for pointers to reference items, but I found it useful also more generally.)

Could this feature be brought back?

]]>Looks good to me. Thanks!!

]]>for when editing is back up

The YouTube link in

Colin McLarty, Grothendieck’s 1973 topos lectures, Séminaire Lectures grothendieckiennes, 3 May (2018) (YouTube video)

no longer works, but this Oct 7, 2018 one does.

https://www.youtube.com/watch?v=5AR55ZsHmKI

It may also appear in topos and maybe elsewhere.

]]>I have now rendered group actions on spheres using the new renderer. I needed to add some further functionality to the latter and to robustify some aspects of it to get it to work, so things are coming along. Please let me know if anything looks wrong on this page. There are a number of things to check: an equation reference for instance. I had particular trouble trying to repair the fact that Instiki, or more probably its underlying Markdown renderer Maruku, was extremely permissive with regard to list syntax, in a way that is not really in accordance with the Markdown spec (albeit the latter is somewhat loosely defined and often somewhat loosely interpreted), and which is not permitted by the new underlying Markdown renderer (a Python library called mistletoe). Thus please especially check that all the numbered lists render correctly.

I am aware of one small issue, namely that any LaTeX in the context menu is not rendering; I will fix this when I get a chance.

]]>It doesn’t seem right, because for example there are infinitely many endofunctors on the free category $B\mathbb{N}$ on the loop on $0$.

]]>Sorry for not having addressed that issue; I had seen it, but had not an opportunity to do it before the migration. I’m happy to do that and it is essentially trivial, so I just need to remember; just remind me if I forget!

]]>Especially encouraged if it’s not mere citing but also includes some associated commentary.

]]>Just to record another reference for when the editing functionality is back:

- Karl H. Hofmann and Sidney A. Morris,
*The Structure of Compact Groups*, De Gruyter Studies in Mathematics**25**(2020) (doi:10.1515/9783110695991)

This textbook is one of the few (?) which makes explicit the decomposition of $L^2(G)$ into irreps – they call it the “Fine Structure Theorem” (3.28).

]]>The idea is that you add the best material you have to offer. If you have thought about and written about it before, then all the better.

]]>If xy-pic is being migrated, I’d like to advertise a suggestion left at GitHub (basically to change “UseTwocells” to “UseAllTwocells” in the preamble, allowing to draw more kinds of shapes). Not a priority, really.

]]>