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

• I have tried to expand the Idea-section at orbit method a little.

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• promted by demand from my Basic-Course-On-Category-Theory-Students I expanded the entry 2-category:

• mentioned more relations to other concepts in the Idea-section;

• added an Examples-section with a bunch of (classes of) examples;

• brief category:people-entry for hyperlinking references

• I have received an email asking for clarification at the (old) entry equivalence of 2-categories, as to the meaning of “essentially full”. I have briefly added a parenthetical “i.e. essentially surjective on hom-categories”. But the entry deserves to be expanded a bit more, maybe somebody feels inspired to do so?

• Added actual definition for pseudofunctor and modified notions, moved discussion from idea section to new discussion section at bottom of page.

• brief category:people-entry for hyperlinking references at tricategory

• starting something, for the moment mainly to record the other result of Brown & Szczarba (dg-algebraic rational homotopy theory for general connected spaces)

• Added to the entry fuzzy dark matter pointer to Lee 17 which appeared today on the preprint server. This is just a concise 2.5 page survey of all the available literature, but as such is very useful. For instance it points out this Nature-article:

• Hsi-Yu Schive, Tzihong Chiueh, Tom Broadhurst, Cosmic structure as the quantum interference of a coherent dark wave, Nature Physics 10, 496–499 (2014) (doi:10.1038/nphys2996)

which presents numerical simulation of the fuzzy dark matter model compared to experimental data.

• Create a stub page.

• Thanks to Karol Szumiło’s answer to my MO question, I have added to Brown representability theorem a mention of the counterexamples for nonconnected pointed spaces and for unpointed spaces (plus a mention of Brown’s abstract categorical version).

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

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• a category:reference-entry

• Page created. Idempotent monoids should be to monoids as idempotent monads are to monads.

I’ve added the examples of idempotent elements in (ordinary) monoids (1), idempotent morphisms in categories (2), solid rings (3), idempotent monads (4), idempotent $1$-morphisms in bicategories (5), and “solid ring spectra” (6) ―What are other examples?

Also, should idempotent monoids have a unit? The examples 1 and 2 I mentioned above don’t, but 3, 4, and 6 do, while whether 5 does or doesn’t seems to vary a bit among the literature (AFAIU).

• Maximilian Doré, Samson Abramsky, Towards Simplicial Complexes in Homotopy Type Theory (pdf)

• starting something

• tried to bring the entry Lie group a bit into shape: added plenty of sections and cross links to other nLab material. But there is still much that deserves to be done.

• I have added pointers to Mikhail Kapranov’s talks on the sphere spectrum in relation to super-algebra, and added some words at the beginning that this was the original motivation for the proposed definition of spectral supergeometry in the entry.

Also I fixed the link to the video recording of Krapranov’s 2013 talk. The previous link no longer worked but there is a YouTube copy of the video. Fixed this also at superalgebra, see there at Kaprananov 13

• Baez and Dolan mainly did the periodic table of k-tuply monoidal n-categories; this article was written like all we did was “slightly distort” some existing table.

• A couple of properties.

• Explain the connection with enriched monads

• brief category:people-entry for hyperlinking references

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• starting something. There is nothing to be seen yet, but I need to save.

• added a brief section (here) on the original “Conner-Floyd orientation”

$\array{ M SU &\longrightarrow& K \mathrm{O} \\ \big\downarrow && \big\downarrow \\ M \mathrm{U} &\longrightarrow& K \mathrm{U} }$
• I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.

I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.

In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes

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

• I added some content in protomodular category. It’s mostly drawn from Bourn’s papers. It will need brushing up, cross-linking, etc.

There are many further related concepts. Don’t know how important they are, e.g., Bourn says

The dual of a topos is arithmetical.

Is that a standard concept? And ’affine categories’?

• Added link to Bourn’s most helpful 2017 textbook From Groups to Categorial Algebra : Introduction to Protomodular and Mal’tsev Categories. Revised reference to the Borceux-Bourn 2004 monograph.

• brief category:people-entry for hyperlinking references