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Anonymous

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The Swiss cheese operad is an analogue of the little disks operad, where disks are replaced by half-disks, which contain both ordinary disks in their interior, as well as half-disks positioned at the flat boundary.

This structure can be organized into an operad in the category of modules over the little disks operad.

Alexander Voronov,

*The Swiss-Cheese Operad*, arXiv:math/9807037.Najib Idrissi,

*Swiss-Cheese operad and Drinfeld center*, arXiv:1507.06844.

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 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.

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An operad is a monoid in the monoidal category of symmetric sequences equipped with the substitution product.

A **module over an operad** is just a right module over this monoid.

Right modules are very different from left modules, the latter are essentially algebras over an operad.

V. A. Smirnov. ON THE COCHAIN COMPLEX OF TOPOLOGICAL SPACES. Mathematics of the USSR-Sbornik 43:1 (1982), 133–144. doi.

Martin Markl,

*Models for operads*, Comm. Algebra 24 (1996), no. 4, 1471–1500. arXiv:hep-th/9411208v1.

I have added pointer to

- Ernesto Lupercio, Bernardo Uribe, Section 7.2 of:
*Gerbes over Orbifolds and Twisted K-theory*, Comm. Math. Phys. 245(3): 449-489. (arXiv:math/0105039, doi:10.1007/s00220-003-1035-x)

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).

Also added pointer to

- Marco Mackaay,
*A note on the holonomy of connections in twisted bundles*, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 1, pp. 39-62. (arXiv:math/0106019, numdam:CTGDC_2003__44_1_39_0)

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…

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]]>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.

]]>added pointer to

- Daniel Freed, Michael Hopkins, Constantin Teleman, Section 2 of:
*Twisted equivariant K-theory with complex coefficients*, Journal of Topology, Volume 1, Issue 1, 2007 (arXiv:math/0206257, doi:10.1112/jtopol/jtm001)

Added related concepts.

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]]>starting something, on the kind of theorems originating with

- Graeme Segal,
*The topology of spaces of rational functions*, Acta Math. Volume 143 (1979), 39-72 (euclid:1485890033)

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.)

]]>brief `category:people`

-entry for hyperlinking references at *Gromov-Witten theory*

added pointer to:

- Albrecht Bertram,
*Stable Maps and Gromov-Witten Invariants*, School and Conference on Intersection Theory and Moduli Trieste, 9-27 September 2002 (pdf)

I have added at *HomePage* in the section *Discussion* a new sentence with a new link:

If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.

I had completly forgotton about that page *Welcome to the nForum (nlabmeta)*. I re-doscivered it only after my recent related comment here.

added this pointer:

- János Kollár, Section 3 of:
*Algebraic hypersurfaces*, Bull. Amer. Math. Soc. 56 (2019), 543-568 (arXiv:1810.02861, doi:10.1090/bull/1663)

added pointer to:

- Igor Shafarevich,
*Basic Algebraic Geometry 1 – Varieties in Projective Space*, Springer 1977, 1994, 2013 (pdf, doi:10.1007/978-3-642-57908-0)

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…

]]>I have added pointer to the arXiv copy to the item

- Daniel Berwick-Evans, Pedro Boavida de Brito, Dmitri Pavlov,
*Classifying spaces of infinity-sheaves*(arXiv:1912.10544)

Added some references at Morse theory.

]]>brief `category:people`

-entry for hyperlinking references at *birational geometry*

brief `category:people`

-entry for hyperlinking references at *Hilbert scheme* and *birational geometry*

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:

- William Fulton, Robert MacPherson,
*A compactification of configuration spaces*, Ann. of Math. (2), 139(1):183–225, 1994 (jstor:2946631)

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

]]>added pointer to today’s

- Roberto Longo,
*The emergence of time*(arxiv:1910.13926)