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## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• Attempt at making a page about defunctionalization. My first new page on nlab, I hope there are no faux pas’s. I noticed the resemblance to the adjoint functor theorem a while back, and several people seemed to find it interesting, so I thought I’d make a page.

• I filled in a bit on the Wightman axioms. I also have a query there about adding an "axiom" environment to the LaTeX/CSS style sheets of nLab. I don't know how to do it on nLab but an axiom environment seems like it might be useful.
• “Covariant presheaf” seems to be a more widely-used name than “copresheaf”, so it’s useful to document it here.

• Add references relating to rewriting.

• Create page, add some initial references. Referenced from the ’category theory’ page.

• Stub for associative n-categories.

• Jamie Vicary is kindly adding information to the $n$Lab on the higher-category-theory-proof-assistant that he and collaborators are developing, at:

And I have changed the page name from lower case “globular” to upper case “Globular” to fit our conventions on entry titles.

Currently, lower case “globular” still redirects to the entry. But if anyone has links to the lower case version from elsewhere, please consider changing them, for eventually the lower case “globular” really ought to go to a page that disambiguates all sorts of globular-related entries on the nLab, such as globe and globular set, etc.

• Created stub for Spin group. Made a mess of explaining why it is so named.

-David Roberts
• I am splitting off an entry classification of finite rotation groups from ADE classification in order to collect statements and references specific to the classification of finite subgroups of $SO(3)$ and $SU(2)$.

Is there a canonical reference for the proof of the classification statement? I find lots of lecture notes that give the proof, but all of them without citing sources or original publications of proofs.

• starting a stub

• Forgot to mention that I started something on Coxeter group. A lot of it is examples, particularly finite reflection groups (where the classification was effectively stated). If someone knows how to draw Coxeter diagrams, those would be great to include.

• Page created, but author did not leave any comments.

• added to icosahedral group discussion of the distinction of definitions as one moves up the Whitehead tower of $O(3)$

$\array{ \mathcal{I} &\hookrightarrow& String_{SU(2)} \\ \downarrow && \downarrow \\ 2 I &\hookrightarrow & Spin(3) = SU(2) \\ \downarrow && \downarrow \\ I \simeq A_5 &\hookrightarrow& SO(3) \\ \downarrow && \downarrow \\ I_h \simeq A_5\times \mathbb{Z}/2 &\hookrightarrow & O(3) }$

[edit: added analogous discussion to octahedral group and icosahedral group ]

• a stub, trying to bring in infrastructure for discussion of the finite subgroups of $O(5)$

• a stub, am trying to bring into place some infrastructure for discussion of the finite subgroups of $O(5)$

• starting a stub, for the moment just collecting references.

Which finite subgroup of $SO(4)$ corresponds to the 120-cell?

• Created opetopic type theory with a bit of explanation based on what I understood based on what Eric Finster explained and demonstrated to me today.

This is the most remarkable thing.

I have added pointers to his talk slides and to his online opetopic type system, but I am afraid unguided exposition to either does not reveal at all the utmost profoundness of what Eric made me see when he explained and demonstrated OTT to me on his notebook. I hope he finds time and a way to communicate this insight.

• created stub for étale morphism of E-∞ rings in order to record the theorem of essential uniqueness of lifts of étale morphism from underlying commutative rings to $E_\infty$-rings (which is crucial for the characterization of the moduli stack of derived elliptic curves, and I have cross-linked with that). But otherwise no content yet, due to lack of leisure.

• A skeleton

• I added a proposition to this subsection which seems valid intuitionistically, but I wouldn’t mind a reality check from someone.

• tried to polish a little and slightly expand model category, starting with the Definition-section and ending with the (new and tiny) Properties section. Added some more subsections and so on.

• Created page with some basic definitions.

• starting something. Not done yet but need to save