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

• brief category:people-entry for hyperlinking references at orbifold K-theory and elsewhere

• I looked at the entry 2-group today and found it strongly wanting. Now I have spent a few minutes with it, trying to bring it into better shape. While I think I did imporve it a little, there is clearly still lots of further room for improvement.

Mainly what I did was add more on the intrinsic meaning and definition, more on the homotopical meaning, and more on the details of how crossed modules present the $(2,1)$-category of 2-groups – amplifying the role of weak equivalences. And brief remarks on how all this generalizes to the case of 2-groups “with structure” hence internal to other $\infty$-toposes than the terminal one.

• Fixed the link for Subtle symmetries and the refined Monster.

• Finally I am starting an entry Platonic 2-group.

For the moment, all it has is the statement of Epa-Ganter 16, prop. 4.1, rephrased as the diagram

$\array{ \mathcal{G}_{uni}[i] &\longrightarrow& \mathbf{B}G_{ADE} &\longrightarrow& \mathbf{B}^3 \mathbb{Z}/{\vert G_{ADE}\vert} \\ \downarrow && \downarrow && \downarrow \\ String(SU(2)) &\longrightarrow& \mathbf{B} SU(2) &\underset{\mathbf{c}_2}{\longrightarrow}& \mathbf{B}^3 U(1) }$
• Initial writeup.

• Started page with a definition.

• Starting this, for the moment just as a bare disambiguation page. But it might make sense to have this here be the entry about finite types in the sense of type theory, and keep the list currently here under “Related entries”

• Finite types have a different meaning in type theory and homotopy type theory.

Anonymous

• Included the condition on sequential (co)limits that the indexing ordinal should be nonzero, which I presume to be the correct convention. (e.g. based on the description they are a special case of filtered colimits)

• books

• am giving this theorem its own stand-alone entry, for ease of hyperlinking to it

• Created page.

• found this old entry, made some little improvements of wording and hyperlinking.

• Created a basic category: people page with link to webpage.

• Added definition of dynkin diagram and the dynkin index for now. will add significance of this index in 4-D gauge theories and instanton physics

• Added some intuition for coskeleta

• Added to derivator the explanation that Denis-Charles Cisinski had posted to the blog.

Zoran, I have made the material you had here the section "References", as this was mainly pointers to the literature. Please move material that you think you should go into other sections.

• starting something

• Creating a New note about the Kakeya Conjecture. Just starting.

Felipe Ponce

• Came across this isolated page and have edited, added links, etc.

• I have added also the statement of the two relative versions of the Serre spectral sequence (here). No details yet.

• Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their interrelatedness. I wasn’t sure what to name this page — or even whether it should be part of some other page — but I like having all these closely related structures described in the same place.

• Added a remark on the codensity monad of the inclusion into all homotopy types.

• created the page for Mealy morphisms and just put in one reference

Tim Hosgood

• Karol Szumiło, Homotopy theory of cofibration categories. Homology Homotopy Appl. 18 (2016), no. 2, 345–357. doi

• Karol Szumiło, Homotopy theory of cocomplete quasicategories. Algebr. Geom. Topol. 17 (2017), no. 2, 765–791. doi

• Krzysztof Kapulkin, Karol Szumiło, Quasicategories of frames of cofibration categories. Appl. Categ. Structures 25 (2017), no. 3, 323–347. doi

• Karol Szumiło, Frames in cofibration categories. J. Homotopy Relat. Struct. 12 (2017), no. 3, 577–616. doi

• Markus Land, Thomas Nikolaus, Karol Szumiło, Localization of cofibration categories and groupoid C∗-algebras. Algebr. Geom. Topol. 17 (2017), no. 5, 3007–3020. doi

• am finally giving $\overline{W}G$ its own entry, for ease of hyperlinking to it

• 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.

• 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 ]

• added pointer to Section 4.2 of:

for computation of the group cohomology

• added statement of subgroup inclusion $Q_8 \subset 2 T$ (here).

• added the statement (here) that of all finite subgroups of $SU(2)$, $Q_8$ is a proper subgroup of the three exceptional ones.

Checking normality of this subgroup, I noticed that there is an issue with another item of the entry here, where it used to claim that a finite group is Hamiltonian precisely of it “contains a copy of $Q_8$”. But this can’t be, can it. I changed it to saying that every Hamiltonian group contains $Q_8$ as a subgroup, which I suppose is what was meant.

[edit: I see now that the statement that I changed back to was made already by Thomas Holder in rev 3, while the statement I removed was made by Thomas in rev 4. Thomas, if you see this, please let me know. ]

• Created a basic category: people page with link to personal website.

• Created a page for delta lens containing a general idea, definition, some examples, and key references.

• I have

• touched the formatting of this ancient entry,

• expanded and streamlined the Idea-section a little,

• added illustrating diagrams for the definition of the sieves appearing in the definition (here) of local epis from a given site

• added the version of the definition for covergages instead of Grothendieck topologies (here, is this in Johnstone?)

• added statement of the proposition that the Cech nerve projection out of a local epi is a local weak equivalence of simplicial presheaves (here)

• Thought I’d begin this stub.

• started an entry on the Borel construction, indicating its relation to the nerve of the action groupoid.

• I've created a new article entitled algebra for a C-C bimodule, a straightforward concept encapsulating both algebras and coalgebras for endofunctors, as well as further generalities besides. There's surely a better name than using "C-C bimodule" (replacing it with "endoprofunctor", perhaps? Although I actually find that less preferable...), for someone to propose or let me know already exists, as the case may be.

(I've also made some small edits to the articles on algebras and coalgebras for endofunctors; in particular, the former had forgotten to define the morphisms of such algebras)

• Changed left' toright’ in one place, and ‘fib rations’ to guess what!

• at simplicial group I added/expanded the section delooping and simplicial principal bundles

I discuss this in revisionistic terms meant to exhibit the simple general underlying structure, and then try to spell out how it corresponds to vaarious explicit constructions in the literature, trying to point out page and verse in May’s “Simplicial objects in algebraic topology” and discuss how that yields what I am discussing.

By the way, did anyone ever find the time to make a sanity check of my query-box claim at decalage that forming decalage in sSet is nothing but forming the standard based path space object?