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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topiccompact ordered space
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active 2 hours ago

- Discussion Type
- discussion topicDisambiguation request for two pages
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active 2 hours ago

Hello. There is possible confusion between the notions of separated set and separated subset, which have different pages and mean different things. Any advice on how to handle this?

Thanks!

- Discussion Type
- discussion topicsaturated set
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active 2 hours ago

- Discussion Type
- discussion topicstably compact space
- Category Latest Changes
- Started by PaoloPerrone
- Comments 2
- Last comment by PaoloPerrone
- Last Active 2 hours ago

- Discussion Type
- discussion topicDuflo isomorphism
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active 3 hours ago

- Discussion Type
- discussion topicKashiwara-Vergne conjecture
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 hours ago

I split some material specific to Kashiwara-Vergne conjecture from Hausdorff series and added more references and a quoted idea from a seminar page. Related to Drinfeld associator (with which it has a serious overlap, especially in references) and few related pages I work on these days.

- Discussion Type
- discussion topicbar and cobar construction
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 5 hours ago

added pointer to

- Dev Sinha, Section 1 in:
*Koszul duality in algebraic topology - an historical perspective*, J. Homotopy Relat. Struct. (2013) 8: 1 (arXiv:1001.2032)

- Dev Sinha, Section 1 in:

- Discussion Type
- discussion topicequivariant Hopf degree theorem
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active 8 hours ago

am finally splitting this off from

*Hopf degree theorem*, to make the material easier to navigate. Still much room to improve this entry further (add an actual Idea-statement to the Idea-section, add more examples, etc.)

- Discussion Type
- discussion topicpermutation representation
- Category Latest Changes
- Started by zskoda
- Comments 101
- Last comment by Urs
- Last Active 8 hours ago

Unfortunately, I need to discuss with you another terminological problem. I am lightly doing a circle of entries related to combinatorial aspects of representation theory. I stumbled accross permutation representation entry. It says that the permutation representation is the representation in category $Set$. Well, nice but not that standard among representation theorists themselves. Over there one takes such a thing – representation by permutations of a

*finite*group $G$ on a set $X$, and looks what happens in the vector space of functions into a field $K$. As we know, for a group element $g$ the definition is, $(g f)(x) = f(g^{-1} x)$, for $f: X\to K$ is the way to induce a representation on the function space $K^X$. The latter representation is called the**permutation representation**in the standard representation theory books like in- Claudio Procesi,
*Lie groups, an approach through invariants and representations*, Universitext, Springer 2006, gBooks

I know what to do approximately, we should probably keep both notions in the entry (and be careful when refering to this page – do we mean representation by permutations, what is current content or permutation representation in the rep. theory on vector spaces sense). But maybe people (Todd?) have some experience with this terminology.

Edit: new (related) entries for Claudio Procesi and Arun Ram.

- Claudio Procesi,

- Discussion Type
- discussion topictopological G-space
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 12 hours ago

added pointer to Bredon 72. Will add this pointer also to various related entries on equivariant homotopy theory

- Discussion Type
- discussion topicone-point compactification
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active 13 hours ago

tried to polish one-point compactification. I think in the process I actually corrected it, too. Please somebody have a close look.

- Discussion Type
- discussion topicheterotic string theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 14 hours ago

added pointer to today’s

- Andrea Fontanella, Tomas Ortin,
*On the supersymmetric solutions of the Heterotic Superstring effective action*(arxiv:1910.08496)

- Andrea Fontanella, Tomas Ortin,

- Discussion Type
- discussion topicPoisson-Lie T-duality
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active 15 hours ago

started a bare minimum at

*Poisson-Lie T-duality*, for the moment just so as to have a place to record the two original references

- Discussion Type
- discussion topicextended probabilistic powerdomain
- Category Latest Changes
- Started by PaoloPerrone
- Comments 7
- Last comment by PaoloPerrone
- Last Active 21 hours ago

- Discussion Type
- discussion topiccobordism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 23 hours ago

A student asked “What is a cobordism?” and I checked and realized that the $n$Lab entry

*cobordism*was effectively empty.So I have now added some basic text in the Idea-section and added a bare minimum of references. Much more should be done of course, but at least now there are pointers.

- Discussion Type
- discussion topiccohomotopy
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active 1 day ago

At the old entry

*cohomotopy*used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.(We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

- Discussion Type
- discussion topicMichael Atiyah
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicGiry monad
- Category Latest Changes
- Started by zskoda
- Comments 30
- Last comment by PaoloPerrone
- Last Active 1 day ago

Added a reference of Robert Furber, Bart Jacobs at Giry monad.

- Discussion Type
- discussion topicM5-MO9 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

need a place to record the references on heterotic NS5-branes as “small Yang-Mills instantons”:

Andrew Strominger,

*Heterotic solitons*, Nucl.Phys. B343 (1990) 167-184 (doi:10.1016/0550-3213(90)90599-9) Erratum: Nucl.Phys. B353 (1991) 565-565 (doi:10.1016/0550-3213(91)90349-3) (spire:)Edward Witten,

*Small Instantons in String Theory*, Nucl.Phys.B460:541-559, 1996 (doi:10.1016/0550-3213(95)00625-7)

So I am finally starting this entry here

- Discussion Type
- discussion topicDp-D(p+4)-brane bound states -- contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicPontrjagin-Thom collapse map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

added to the Idea-section (here) the description of PT-collapse as the function that assigns “asymptotic distance form the submanifold”, an illustrating graphics, and a comment that this represents the Cohomotopy charge of the submanifold

- Discussion Type
- discussion topiccohomotopy charge map
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicvaluation (measure theory)
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by PaoloPerrone
- Last Active 1 day ago

- Discussion Type
- discussion topicmonads of probability, measures, and valuations
- Category Latest Changes
- Started by PaoloPerrone
- Comments 3
- Last comment by PaoloPerrone
- Last Active 1 day ago

- Discussion Type
- discussion topicmultiplicative unitary
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active 1 day ago

I am starting a page about the pentagon relation for multiplicative unitaries and related mathematics. The page for pentagon relation should be a separate page, as one does not really need the real forms and unitarity condition for the pentagon to work; this pentagon relations is sometimes called pentagon equation. $n$Lan uses pentagon equation as a redirect to pentagon identity from the axioms of (coherent) monoidal category, which is usually called pentagon identity indeed, and the terms relations and equation are more used in the context of dilogarithms, quantum groups, operator algebras and alike subjects, all related. The pentagon coherence is in fact related to all of these in a large subset of cases which can be directly expressed categorically, but the literature is quite different in flavour and eventually I will build 3 different pages with redirects and other superstructure, and references to the related terms like Drinfeld associator.

- Discussion Type
- discussion topicVerlinde formula
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active 2 days ago

I added few references, e.g. on the logarithmic CFT case. Maybe the entry should be fused with fusion ring, I see no reason to discuss it separately, the entries are both sketchy and have little material so far.

- Discussion Type
- discussion topicDirac charge quantization
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicmoduli space of monopoles
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 2 days ago

starting something, but nothing here yet. For the moment this is just a home for

- Michael Atiyah, Nigel Hitchin,
*The geometry and dynamics of magnetic monopoles*M. B. Porter Lectures. Princeton University Press, Princeton, NJ, 1988 (jstor:j.ctt7zv206)

- Michael Atiyah, Nigel Hitchin,

- Discussion Type
- discussion topicrational model of mapping space
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicconfiguration space of points
- Category Latest Changes
- Started by Tim_Porter
- Comments 69
- Last comment by Urs
- Last Active 3 days ago

I fixed a link to a pdf file that was giving a general page, and not the file!