added at *core* the remark that the core is right adjoint to the forgetful functor $Grpd \to Cat$.

more examples

]]>Added overview of a different notion common in representation theory of non-commutative algebras. This is my first nLab edit; please excuse (and fix) any errors of house style or formatting.

David Speyer

]]>more elementary language for $\Delta_+$

Yuxi Liu

]]>Started adding a description of the Duskin nerve (together with some pictures), following Johnson–Yau’s new book.

]]>Fixed a link

]]>Fixed dodgy formating

]]>I fixed a trivial typo in adjoint functor theorem but left wondering about this:

… the limit

$L c := \lim_{c\to R d} d$over the comma category $c/R$ (whose objects are pairs $(d,f:c\to R d)$ and whose morphisms are arrows $d\to d'$ in $D$ making the obvious triangle commute in $C$) of the projection functor

$L c = \lim_{\leftarrow} (c/R \to D ) \,.$

I don’t really understand this (and while I could figure it out, it’s probably not good to make readers do so). At first it sounds like someone is saying “the limit $L c$ over the comma category of the projection functor $L c$”, which would be circular. But it must be that both formulas are intended as synonymous definitions of $L c$. At that point one is left wondering why one has a backwards arrow under it and the other does not. I guess old-fashioned people prefer writing limits with backwards arrows under them, so someone is trying to cater to all tastes? I think it’s better in this website to use $lim$ and $colim$ for limit and colimit.

I could probably guess how to fix this, but I won’t since I might screw something up.

]]>I have spelled out the proof (here) of the claim from

- Michel Dubois-Violette, Ivan Todorov,
*Exceptional quantum geometry and particle physics II*(arXiv:1808.08110)

that the stabilizer in the automorphism group $F_4$ of the octonionic Albert algebra “of a 4d Minkowski subspace” happens to be the *exact* gauge group of the standard model of particle physics.

I added a bit to the section on the ultrafilter monad in ultrafilter. This could stand to be fleshed out still more. The immediate reason for my editing here was to put down the notion of “compact Hausdorff object” (which is used in a remark at BoolAlg).

]]>started some minimum, prodded by the suggestion in today’s replacement

- Bhavesh Chauhan, Subhendra Mohanty,
*A common leptoquark solution of flavor and ANITA anomalies*(arXiv:1812.00919)

that leptoquarks could not only explain the flavour anomalies but also the anomalous events seen last year by the ANITA experiment

]]>Added

]]>For a way to study ultraproducts in a homotopical setting see

- Tobias Barthel, Tomer Schlank, Nathaniel Stapleton,
Chromatic homotopy theory is asymptotically algebraic, (arXiv:1711.00844)

worked on [[space and quantity]] a bit

tried to polish the introduction and the Examples-section a bit

added a section on the adjunction with a detailed end/coend computation of the fact that it is an adjunction.

I ended up collecting some references at *string phenomenology* and accompanying them with a bit of text

at effective quantum field theory I have started writing an Idea-section and added more reference

]]>Correct the characterization of nerves of groupoids.

]]>this entry is meant to contain a bare sub-section, to be `!include`

-ed into relevant entries, such as at *equifibered natural transformation*, at *(infinity,1)-topos* and maybe at *descent*, etc.

equifibered natural transformation misses references. I’ve traced cartesian natural transformation back to: Street - the petit topos of globular sets which refers to: Carboni, Johnstone - Connected limits, familial representability and Artin glueing unfortunately, I do not have access to the latter.

Is this the best source?

]]>TODO: section 4 of the paper, and examples.

mattecapu

]]>I have re-written the content at *differentiable manifold*, trying to make it look a little nicer. Also gave *topological manifold* some minimum of content.

I thought it better to use $pred(n)$ rather than $n -1$ in the addition, since it’s supposed to apply to $\infty$.

]]>I added the suggestion that there is a version for HoTT.

]]>started an index of the keywords in Ravenel’s book *Complex cobordism and stable homotopy groups of spheres*.

So far I got through most of the first chapter. Touched many of the entries involved.

The main entries *chromatic spectral sequence* and *EHP spectral sequence* are stubs for the moment.

New page, covering both French and English definitions, as well as limits of relations and spans, and restricted versions.

]]>Page created, but author did not leave any comments.

Yuxi Liu

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