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In context of size issues on admissible structures (in the sense of DAG V) I wondered which closure properties (e.g. obviously its closed under pullbacks along relatively k-compact morphisms) the class of relatively k-compact (for a regular cardinal k) morphisms in a (∞,1)-category satisfies. Is there any reference concerning this?
I needed an entry that lists references on twisted K-homology, so I created one. This made me notice that we currently lack an entry K-homology. I can try to create a stub for that a little later…
Created saturated class of limits.
created symplectic singularity…
… for the moment just to record references and such as to satisfy links at symplectic duality.
the link to the picture in the entry Charles Wells is broken. Does anyone know how to fix it or have an alternative picture?
stub for adjoint representation
Perhaps we need a page on Jean-Louis Koszul, and possibly an agreement on terminology / names for entries. Ben has created a page called Koszul, but usually single names like that would be used for the ’person’ page of that mathematician, so … The term in in any case (as adjective) is also used in various other contexts e.g. for operads, so possibly there needs to be some rationalisation. My thought would be to combine a page on Koszul (and the Wikipedia (English) page on him is poor, and includes some very poor translation from the French ) with a certain amount of disambiguation, however I am not an expert on things ’Koszul’ and this may not be the most efficient way to go.
I created orbifold groupoids with some classes of groupoids whose elements I like to think of as ‘‘orbifold groupoids‘‘. It would be nice to have a discussion of the interelation of these classes there, too.
I rewrote the Idea-section of geometry (for structured (infinity,1)-toposes), tring to make it more to the point and much shorter. Also highlighted the relation to oo-algebraic theories.
quick note canonical model structure on Operad.
Needs to be expanded and equipped with commented cross-links to the related entries. Later.
added the definition to Beilinson-Deligne cup product.
Also expanded the list of references here and at Deligne cohomology.
am starting an entry operadic (∞,1)-Grothendieck construction
I created Pi-closed morphism. This material is in differential cohomology in a cohesive (∞,1)-topos, too.
am starting an entry Cartesian fibration of dendroidal sets
I was in the process of creating an entry for Cartesian fibration of dendroidal sets, when by accident I suddently discovered that the degree-1 case of this had been considered before, by Claudio Hermida. So now I have also created a brief entry
created a stub for super parallel transport, for the moment just so as to record Florin Dumitrscu’s recent preprint
at associative operad I have made explict the links to symmetric operad and planar operad, as need be.
I thought it would be useful to supplement the entry operad with entries symmetric operad and planar operad, that amplify a bit more on the specifics of these respective flavors of the general notion, and that will allow us in other entries to link specifically to one of the two notions, when the choice is to be made explicit.
So far I have written (only) an Idea-section at symmetric operad with some comments.
To be expanded.
Started the article parity complex.
I have created a bunch of stub entries such as iterated loop space object with little non-redundant content for the moment. I am filling the k-monoidal table. Please bear with me for the time being, while I add stuff.
have created an entry k-monoidal table to be used for inclusion into the entries that it organizes (see for instance at infinite loop space).
Will now create at least stubs for the missing links.
I have created an entry on the Steinberg group of a ring . The entry includes the Whitehead lemma.
New entries operator topology (for now redirecting also strong operator topology etc.) and unitary representation. Changes at projection measure (the sigma algebra does not need to be the sigma algebra of Borel subsets on a topological space!) and spectral measure. At some point one should add some crosslinks from/to other entries in functional analysis but I am on slow/expensive connection now, hence will restrain to more substantial (in content sense) edits.
Labbified an MO discussion at coproduct-preserving representable.
Created identity component, and added some little remarks to open map and quotient space.
just for completeness, I have created an entry almost connected topological group.
There is a strange glitch on this page: the geometric realization of a cubical set (see geometric realizationealization) below) tends to have the wrong homotopy type:
That is what appears but is not a t all what the source looks like:
the geometric realization of a cubical set (see [geometric realization](#geometric realization) below) tends to have the wrong homotopy type:
What is going wrong and how can it be fixed?
Another point : does anyone know anything about symmetric cubical sets?
Added to normal subgroup a section Normal morphisms of ∞-groups.
I am slowly starting to add stuff at exceptional geometry
I made some edits at classifying topos to correct what I thought were some inaccuracies. One is that simplicial sets classify interval objects, but offhand I didn’t see the exact notion of linear interval over at interval object that would make this a correct sentence. In any event, I went ahead and defined the notion of linear interval as a model of a specified geometric theory.
The other is for local rings. I think when algebraic geometers refer to a sheaf of local rings, they refer to a sheaf of rings over a (sober) space all of whose stalks are local. I wasn’t sure that description would be kosher for a general (Grothendieck) topos since there may not be any “stalks” (i.e., points ) to refer to. In any case, it seems to me safer to give the geometric theory directly.
Matan Prezma kindly pointed out the he has an article with a correction to what used to be prop. 2 at model structure on cosimplicial simplicial sets. (One has to use restricted totalization instead of ordinary totalization.)
I have corrected this and added the reference.
I also added to the entry a remark that makes the relation to descent objects explicit. Right now this is remark 2.
New pages: 2-trivial model structure and mixed model structure.
New page factorization system over a subcategory.
Split measurable subset and measurable function (unfinished) from sigma-algebra and measurable space. Also added to sigma-ideal. Still need to split some things from measure space.
I have created a stub entry for A. Suslin. Can someone add in the Russian original of his name please, as I do not know if the Wikipedia version is correct?
Some time ago, I split Cheng space from measurable space, but I never announced it here (nor removed if from the list of things to do at the latter). Note: Henry Cheng, not Eugenia Cheng.
I added a brief equivalence between two notions of characters of profinite groups that I spotted on MO.
looks like I started extremum
(I wanted minimum not to be gray at higher dimensional Chern-Simons theory…)
I added a section to simplicial set remarking on their status as a classifying topos, and a sentence to classifying topos (in the section “For objects”) recording the answer to this question.
I have created an entry Wu class.
At the end I have also included an “Applications”-section with comments on Wu classes in the definition of higher Chern-Simons functionals. That eventually deserves to go in a dedicated entry, but for the moment I think it is good to have it there, as it is a major source of discussion of Wu structures in the maths literature, quite indepently of its role in physics.
I added links to the horizontal categorifications in group object and created groupoid object.
In groupoid object in an (infinity,1)-category I read the conspicious statement: ”an internal ∞-group or internal ∞-groupoid may be defined as a group(oid) object internal to an (∞,1)-category C with pullbacks” - but this terminology seems to hinder distinguishing between them and ∞-groupoid objects in (∞,1)-categories.
After Mike’s post, scone was created. But I see at Freyd cover it says
The Freyd cover of a category – sometimes known as the Sierpinski cone or “scone” – is a special case of Artin gluing
Are they synonyms?
Have created a table of contents descent and locality - contents.
Am including this now as a “floating TOC” into the relevant entries.
I am just hearing about the Alfsen-Shultz theorem about states on C*-algebras, so I started a stub to remind me. Still need to track down the reference and the details.
I went through locale and made some of the language consistent throughout the article. Also I added a new section, Subsidiary notions, to which I intend to add.
started a stub entry Toposes on the category (2-category) of all toposes. But nothing much there yet.
I have put some content into the entry relative cohomology
stub for analytic manifold
when creating a stub entry local Langlands conjectures I noticed that it has already become hard to know which entries on the Langlands program we already have. I always take this as a sign that a summary table of contents is called for. So I started
Langlands correspondence – contents
and added it as a “floating table of contents” to the relevant entries.
(Even though all of these entries are still more or less stubs.)
I noticed that there was some wild formatting at building. I have tried to tame it a bit.
a reference on non-commutative analytic spaces (Berkovich style)
started analytic spectrum (redirecting Berkovich spectrum)
I have started a table of contents measure theory - contents and started adding it as a floating toc to the relevant entries
currently the bulk of the entry analytic geometry is occupied by a long section on “Holomorphic functions of several complex variables”. Should that not better be moved to some dedicated entry of its own? Any opinions?
I created branched manifold -linked from orbifold- with a definition from ”expanding attractors” by Robert F. Williams (1974) quoted in wikipedia. This description is -as it stands- not precisely compatible to that given in Dusa McDuffs ”Groupoids, Branched Manifolds and Multisections” which I am rather interested in. So I plan to comment on this as a side note in the -yet to be written-article orbifold groupoid.