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Added some basic examples from HTT. There doesn’t seem to be a page for the corresopnding 1-categorical notion. This notion is used pretty heavily in -category theory, but it’s not so familiar from 1-category theory. But I’d have to think a 1-categorical treatment exists somewhere, right?
thought we needed stem.
Also added more references at stable homotopy groups of spheres
have added pointer to
Charles Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001), 973-1007 (arXiv:math/9811037, doi:10.1090/S0002-9947-00-02653-2)
Julia Bergner, Three models for the homotopy theory of homotopy theories, Topology Volume 46, Issue 4, September 2007, Pages 397-436 (arXiv:math/0504334, doi:10.1016/j.top.2007.03.002)
Hello,
I noticed DFT page has not been updated in a while and I added a couple of sections: some sketchy introductory material (analogy between Kaluza-Klein and DFT) and a little insight about a more rigorous geometrical formulation of DFT.
It is still quite sketchy but I would be happy to refine it.
PS: this is my first edit, I hope I played by the rules. And thank you all for this wiki
Luigi
added (here) statement that the e-invariant is Todd class of cobounding (U,fr)-manifolds
brief category:people-entry for hyperlinking references at singular cohomology
edited and expanded slightly at singular cohomology -- but that entry is far frombeing satisfactory.
In particular I moved the big query box to the bottom and added some remarks and pointers.
I made Andrei Kolmogoroff a redirect to this page
I do not understand why this is a separate entry from Grothendieck topology.
Should this entry be merged into Grothendieck topology?
am too tired to do it now, but on occasion of an MO discussion:
remind me to insert at smooth manifold the statement and proof that smooth manifolds are equivalently the locally representable sheaves on CartSp (more precisely: the -schemes).
brief category:people-entry for hyperlinking references at tensor network, holographic entanglement entropy, and quantum error correcting codes
starting some minimum, but for the moment just to make links work at Atiyah-Bott-Shapiro orientation, Conner-Floyd isomorphism and cobordism theory determining homology theory
created cobordism theory determining homology theory with the basic references (any more results along these lines?), also added a brief cross-link paragraph at Landweber exact functor theorem.
I couldn’t think of a better title, suggestions are welcome.
a bare minimum, to go along with quantum Hall effect and spin Hall effect, etc.
brief category:people-entry for hyperlinking references at quantum Hall effect
brief category:people-entry for hyperlinking references at quantum Hall effect
a bare minimum, to go along with quantum spin Hall effect
brief category:people-entry for hyperlinking references at quantum Hall effect
polished and expanded Ehresmann connection
brief category:people-entry for hyperlinking references at Hall effect
brief category:people-entry for hyperlinking references at quantum spin Hall effect
brief category:people-entry for hyperlinking references at quantum spin Hall effect
brief category:people-entry for hyperlinking references at quantum spin Hall effect and graphene
brief category:people-entry for hyperlinking references at quantum spin Hall effect and graphene
started a stub for projective space
I intend to considerbly expand the story at Atiyah Lie groupoid. But this afternoon I didn't get as far as I intended to, and now I have to quit and visit my parents. So this is to be continued. But so far I did this:
split off Atiyah Lie algebroid from Atiyah Lie groupoid
created a section Relation to differential nonabelian cohomology at Atiyah Lie groupoid that states a claim on how the Atiyah Lie groupoid fits into the story of nonabelian groupoid cohomology -- I wanted to type the proof, too, but ran out of time. Either someone takes it as an exercise and provides the proof, or I'll do so myself later today (or tomorrow)
created a stub for nonabelian groupoid cohomology. There exists a nice reference on "groupoid Schreier theory" that should go there, but I don't have time for that now
created inner automorphism 2-group to provide some background information needed in the statement of the above claim
brief category:people-entry for hyperlinking references at quantum programming language and Quipper
brief category:people-entry for hyperlinking references at quantum programming language and Quipper
brief category:people-entry for hyperlinking references at quantum programming language and Quipper
brief category:people-entry for hyperlinking references at Quipper, dependent linear type theory and quantum programming
brief category:people-entry for hyperlinking references at quantum programming and dependent linear type theory
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<p>I added a statement to <a href="https://ncatlab.org/nlab/show/finite+category">finite category</a> that needs blessing by the experts.</p>
<blockquote>
For any <a href="https://ncatlab.org/nlab/show/finite+category">finite category</a> <img src="/extensions/vLaTeX/cache/latex_ca43fb5496104dcafda44acbe4014b0e.png" title="C" style="vertical-align: -20%;" class="tex" alt="C"/>, there is a <a href="https://ncatlab.org/nlab/show/directed+graph">directed graph</a> <img src="/extensions/vLaTeX/cache/latex_0643966166b879e3e23697a6b846efd7.png" title="G" style="vertical-align: -20%;" class="tex" alt="G"/> such that its <a href="https://ncatlab.org/nlab/show/quiver">quiver</a> <img src="/extensions/vLaTeX/cache/latex_488df68f0543043cfe8c6e7d68900662.png" title="Q(G)" style="vertical-align: -20%;" class="tex" alt="Q(G)"/> is equivalent to <img src="/extensions/vLaTeX/cache/latex_ca43fb5496104dcafda44acbe4014b0e.png" title="C" style="vertical-align: -20%;" class="tex" alt="C"/>.
</blockquote>
<p>I wanted to say "is equal to" but was scared in this crowd :)</p>
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at relation, right at the beginning, I have added remarks that relations are special cases of correspondences – namely the (-1)-truncated correspondences – and that the composition of correspondences induces the composition of relations, under postcomposition with (-1)-truncation. Added a similar remark also to the relevant Properties-section further below.
Then I have tried to cross-link the relevant relational/correspondency entries here a bit more. But don’t really have the leisure.
a bare list of references, to be !include-ed into the References-lists of relevant entries (such as at anyon and quantum Hall effect) for ease of updating and synchronizing
brief category:people-entry for hyperlinking references at anyon and topological quantum computation
brief category:people-entry for hyperlinking references at anyon and topological quantum computation
a stub, to go alongside topological insulator. For the moment just some references
had occasion to check out the state of the art in braid group cryptography.
This page is a bare list of references, briefly commented, to be !inlude-ed into the lists of references at the relevant entries, such as at braid group and cryptography.
I came across this page infinitesimal singular simplicial complex not rendering. How do you look inside to try to fix it?
Added