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

• Introduced the notion of derivation relative to a group homomorphism which can sometimes be a neat notion to have when discussing relative abelianisations.

• there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).

I have added a remark on this in the $(g-2)$-entry here and also at quantum gravity here.

• Starting something. Not done yet, but need to save.

• added to groupoid a section on the description in terms of 2-coskeletal Kan complexes.

• Adjusted the wording of the Idea-section for clarity and flow, and hyperlinked more of the technical terms.

Rongmin Lu

• Todd,

when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

Thanks!

• started adding something (the example of the Hopf fibration and some references).

What’s a canonical reference on the Whitehead products corresponding to the Hopf fibrations? Like what is an original reference and what is a textbook account?

• Created page, mainly to record my understanding of the issue involving strong normalization, or lack thereof, for explicit substitutions.

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

• I made the former entry "fibered category" instead a redirect to Grothendieck fibration. It didn't contain any addition information and was just mixing up links. I also made category fibered in groupoids redirect to Grothendieck fibration

I also edited the "Idea"-section at Grothendieck fibration slightly.

That big query box there ought to be eventually removed, and the important information established in the discussion filled into a proper subsection in its own right.

• added to Grothendieck construction a section Adjoints to the Grothendieck construction

There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.

There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.

• I added more info on pseudo double categories and double bicategories to double category. I also simplified the picture of a square, which had been bristling with scary unnecessary detail. There's a slight blemish in the left vertical arrow, which I can't see how to fix.
• I came across a reference to these, so started something.

• I rescued combinatory logic from being a “my first slide” spam and gave it some content, mainly to record the fact (which I just learned) that under propositions as types, combinatory logic corresponds to a Hilbert system.

I feel like there should be something semantic to say here too, like $\lambda$-calculus corresponding to a “closed, unital, cartesian multicategory” (a cartesian multicategory that is “closed and unital” as in the second example here) and combinatory logic corresponding to a closed category that is also “cartesian” in some sense. Has anyone defined such a sense?

Relatedly, is there a notion of “linear combinatory logic” that would correspond to ordinary (symmetric) closed categories? My best guess is that instead of $S$ and $K$ you would have combinators with the following types:

$(B\to C) \to (A\to B) \to (A\to C)$ $(A \to (B\to C)) \to B \to A\to C$

coming from the two ways to eliminate a dependency in $S$ to make it linear ($K$ is irreducibly nonlinear). These are of course the ways that you express composition and symmetry in a closed category.

• As i have obtained everything from MYSELF AS IM THE GLOBAL SOLO DADABASE ACROSS the world being taken away from me AND HES ON A MISSION AND I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with

Anonymous

• I updated a link on FGA explained to one of the chapters, to point to the arXiv version (the one on constructing Hilbert and Quot schemes). I also added a link to the conference page itself, which has links to scans of lecture notes, as the direct lecture notes links seem to be broken.

• starting something – not done yet, but need to save

• a stub, for the moment

• brief category:people-entry for hyperlinking references

• somebody asked me for the proof of the claim at canonical topology that for a Grothendieck topos $\mathbf{H}$ we have $\mathbf{H} \simeq Sh_{can}(\mathbf{H})$.

I have added to the entry pointers to the proof in Johnstone’s book, and to related discussion for $\infty$-toposes. Myself I don’t have more time right now, but maybe somebody feels inspired to write out some details in the nLab entry itself?

• for completeness, with pointer to

• Alexander Grothendieck et al., 16.5.15 in: Éléments de géométrie algébrique IV_4. Étude locale des schémas et des morphismes de schémas (Quatrième partie) Inst. Hautes Études Sci. Publ. Math. 32 (1967), 5–361. Ch.IV.§16–21 (numdam:PMIHES_1967__32__5_0)
• a stub, for the moment just so as to give a home to

• William Lawvere, Functional Remarks on the General Concept of Chaos , IMA reprint 87, 1984 (pdf)
• Added some discussion (here) of chaotic groupoids on groups as models for their universal principal bundle.

I have now expanded to:

You may read this as the characterization of adjoint functors via universal arrows (via this prop.)…

• a bare list of entries on $(n,r)$-toposes, for varying $(n,r)$, to be !include-ed under “Related concepts” in all relevant entries, for ease of synchronizing the cross-linking

• added cross-links of this ancient entry with higher topos theory and with 2-topos etc.

Notice that there is an old unresolved discussion box here.

• Started something here.

• added pointer (below a new Proposition-environment here) to where Paré states/proves the characterizations of L-finite limits (namely on his p. 740, specifically in his Prop. 7 – this also makes clear which typo the footnote is about).

Similarly I added pointer (below a new Remark-environment here) to where Paré discusses the relation to K-finitness (namely the next page), together with attribution to Richard Wood.

• Mentioned Pos.