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

• stub for internal site. Hope to expand this later, but am out of time now.

Here is something I need to figure out in this context: over at the stub smooth super infinity-groupoid I thought better about what I should be doing there. I think I should take the idea that we are to be working over the base topos of sheaves over superpoints more seriously than I did so far.

Here is what I currently think one needs to do:

1. consider the base topos $\mathrm{Sh}\left(\mathrm{SuperPoint}\right)$ of presheaves on superpoints

2. this has a canonical line object $ℛ\in \mathrm{Sh}\left(\mathrm{SuperPoint}\right)$ which is such that the internal ordinary $ℛ$-linear algebra is externally traditional superalgebra.

3. Define an internal site $\mathrm{sCartSp}$ whose objects are the ${ℛ}^{n}$s and whose morphisms are those morphisms in $\mathrm{Sh}\left(\mathrm{SuperPoint}\right)$ that are smooth according to the Schwarz-Molotkov-version of supermanifolds, as discussed there.

4. Then defined smooth super $\infty$-groupoids to be the internal $\infty$-sheaves on $\mathrm{sCartSp}$.

I am beginning to think that this is the right way to go. But I need to understand better what this definition will unwind to in detail.

• For some reason, we never had map redirect to function, but now we do. Same with mapping.

This may or may not be the best behaviour. We might actually want a page on how people distinguish these words, such as in topology (‘map’ = continuous map but ‘function’ = function, maybe).

• started field (physics).

So far there is an Idea-section, a general definition with some remarks, and the beginning of a list of examples, which after the first spelled out (gravity) becomes just a list of keywords for the moment.

More later.

• Looking at the list there at twisted cohomology is the word ‘getsted’???? does anyone remember what the word was meant to be?!

• Created binary Golay code. The construction is a little involved, and I haven’t put it in yet, because I think I can nut out a nicer description. The construction I aim to describe, in slightly different notation and terminology is in

R. T. Curtis (1976). A new combinatorial approach to M24. Mathematical Proceedings of the Cambridge Philosophical Society, 79, pp 25-42. doi:10.1017/S0305004100052075.

• Some stuff at Mathieu group, including the fact there are several of them and references to the binary Golay code, of which the largest Mathieu group is the automorphism group.

• Created Moufang loop and some links. It would be good to update the proof that the tangent bundle of a Lie group is trivial to include the case of the tangent bundle of a smooth Moufang loop.

• created Cahiers topos.

Do I understand correctly that this gadget is named after the journal that Dubuc’s original article appeared in? What a strange idea.

• added to the list of References at poset of commutative subalgebras the following article

• Jan Hamhalter, Isomorphisms of ordered structures of abelian ${C}^{*}$-subalgebras of ${C}^{*}$-algebras, J. Math. Anal. Appl. 383 (2011) 391–399 (journal)

kindly pointed out to me by Andreas Döring. This generalizes Döring’s result already discussed there from von Neumann algebras to more general ${C}^{*}$-algebras.

• Several recent updates to literature at philosophy, the latest being

• Mikhail Gromov, Ergostructures, Ergologic and the Universal Learning Problem: Chapters 1, 2., pdf; Structures, Learning and Ergosystems: Chapters 1-4, 6 (2011) pdf

which is more into cognition and language problem, but still very relevant, and by a top mathematician. As these 2 are still manuscripts I put them under articles, though I should eventually classify those as books…

• at quantum observable there used to be just the definition of geometric prequantum observables. I have added a tad more.

• I found the section-outline of the entry distribution was a bit of a mess. So I have now edited it (just the secion structure, nothing else yet):

a) There are now two subsections for “Operations on distributions”,

b) in “Related concepts” I re-titled “Variants” into “Currents” (for that’s what the text is about) and gave “Hyperfunctions and Coulombeau distributions” its own subsection title.

c) split up the References into “General” and “On Coulombeau functions”.

(I hope that this message is regarded as boring and non-controversial.)

• created homotopical structure on C*-algebras , summarized some central statements from Uuye’s article on structure of categories of fibrant objects on ${C}^{*}\mathrm{Alg}$.

• added to some relevant entries a pointer to

• I expanded proper model category a bit.

In particular I added statement and (simple) proof that in a left proper model category pushouts along cofibrations out of cofibrants are homotopy pushouts. This is at Proper model category -- properties

On page 9 here Clark Barwick supposedly proves the stronger statement that pushouts along all cofibrations in a left proper model category are homotopy pushouts, but for the time being I am failing to follow his proof.

(??)

• created entries trialgebra and Hopf monoidal category

also expanded the Tannaka-duality overview table (being included in related entries):

to contain the first entries of the corresponding “higher Tannaka duality” relations

• Hilbert C*-module

(brushed up the definition, added four basic classes of examples)

• added to Hilbert bimodule a pointer to the Buss-Zhu-Meyer article on their tensor products and induced 2-category structure.