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• I reorganized linearly distributive category by moving the long block of history down to the bottom, adding an “Idea” section and a description of how $*$-autonomous categories give rise to linearly distributive ones and linearly distributive ones give rise to polycategories. I also cross-linked the page better with polycategory and star-autonomous category.

• I pasted in something Mike wrote on sketches and accessible models to sketch. But now it needs tidying up, and I’m wondering if it might have been better placed at accessible category. Alternatively we start a new page on sketch-theoretic model theory. Ideas?

• added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)

• 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

• I guess it should read as “one defines the (Serre) quotient category $A/T$ as the one having the same objects as $A$ and ….” and not ” … same objects as $T$… ” Similarily in the line following the line mentioned here.

Anonymous

• starting something, on the kind of theorems originating with

Nothing to be seen here yet, but I need to save. (Am not sold on the entry title, except that “topology” is not really the right term here.)

• a bare subsection with a list of references, to be !include-ed into the References-section of relevant enties, such as at triangulation and at triangulation theorem, for ease of synchronizing

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

• I think we should expand this list of languages!

Anonymous

• I gave regular cardinal its own page.

Because I am envisioning readers who know the basic concept of a cardinal, but might forget what “regular” means when they learn, say, about locally representable category. Formerly the Lab would just have pointed them to a long entry cardinal on cardinals in general, where the one-line definition they would be looking for was hidden somewhere. Now instead the link goes to a page where the definition is the first sentence.

Looks better to me, but let me know what you think.

• I have added pointer to

Their Prop. 7.2.2 is verbatim the characterization that BCMMS made the definition of “bundle gerbe module” a month and a half later (except that LU focus on open covers instead of more general surjective submersions, but that’s not an actual restriction and in any case not the core of the definition).

which essentially recovers Lupercio & Uribe’s Def. 7.2.1.

From the arXiv timestamps I gather that it must have been an intense couple of weeks for all these auhtors in spring 2001. But Lupercio & Uribe came out first, by a fair margin. And in equivariant generality, right away…

• starting some minimum

• I have been working on the entry twisted bundle.

Apart from more literature, etc. I have started typing something like a first-principles discussion: first a general abstract definition from twisted cohomology in any cohesive $\infty$-topos, then unwinding this in special cases to obtain the traditional cocycle formulas found in the literature.

Needs more polishing here and there, but I have to pause now.

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

• Albrecht Bertram, Stable Maps and Gromov-Witten Invariants, School and Conference on Intersection Theory and Moduli Trieste, 9-27 September 2002 (pdf)
• Have added a bunch of references to this entry.

Question: What precisely can one say about the relation between the topological space underlying the Hilbert scheme of points of $\mathbb{C}$ and/or $\mathbb{C}^2$, and the Fulton-MacPherson compactification of the corresponding configuration spaces of points?

There is commentary in just this direction on p. 189 of:

but it remains unclear to me what exactly the statement is, in the end.

• added to Eckmann-Hilton argument the formal proposition formulated in any 2-category.

BTW, doesn’t anyone have a gif with the nice picture proof?

• A stub.

• Just heard a nice talk by Simon Henry about measure theory set up in Boolean topos theory (his main result is to identify Tomita-Takesaki-Connes’ canonical outer automorphisms on $W^\ast$-algebras in the topos language really nicely…).

I have to rush to the dinner now. But to remind myself, I have added cross-links between Boolean topos and measurable space and for the moment pointed to

• Matthew Jackson, A sheaf-theoretic approach to measure theory, 2006 (pdf)

for more. Simon Henry’s thesis will be out soon.

Have to rush now…

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