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- Discussion Type
- discussion topicGaussian elimination
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active 2 minutes ago

- Discussion Type
- discussion topicinverse matrix
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active 1 hour ago

- Discussion Type
- discussion topicSchur complement
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 1 hour ago

New entry to complement matrix inverse.

- Discussion Type
- discussion topicabelian sheaf cohomology
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 6
- Last comment by zskoda
- Last Active 2 hours ago

- Discussion Type
- discussion topicquasideterminant
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active 3 hours ago

- Discussion Type
- discussion topicunstable K-theory
- Category Latest Changes
- Started by perezl.alonso
- Comments 5
- Last comment by perezl.alonso
- Last Active 20 hours ago

- Discussion Type
- discussion topicDimitry A. Leites
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicsupermanifold
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active 1 day ago

I have added a little bit to supermanifold, mainly the definition as manifolds over superpoints, the statement of the equivalence to the locally-ringed-space definition and references.

- Discussion Type
- discussion topicVictor A. Toponogov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicdifferential geometry of curves and surfaces
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 1 day ago

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

added this quote to before the Idea-section:

In the wake of the movement of ideas which followed the general theory of relativity, I was led to introduce the notion of new geometries, more general than Riemannian geometry, and playing with respect to the different Klein geometries the same role as the Riemannian geometries play with respect to Euclidean space. The vast synthesis that I realized in this way depends of course on the ideas of Klein formulated in his celebrated Erlangen programme while at the same time going far beyond it since it includes Riemannian geometry, which had formed a completely isolated branch of geometry, within the compass of a very general scheme in which the notion of group still plays a fundamental role.

[Élie Cartan 1939, as quoted in Sharpe 1997, p. 171]

- Discussion Type
- discussion topicRiemannian geometry
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 1 day ago

added pointer to:

- John M. Lee,
*Riemannian manifolds. An introduction to curvature*. Graduate Texts in Mathematics 176 (1997), Springer. ISBN: 0-387-98271-X. Second Edition (retitled):*Introduction to Riemannian Manifolds*(2018), Springer. ISBN: 978-3-319-91754-2 (doi:10.1007/978-3-319-91755-9)

- John M. Lee,

- Discussion Type
- discussion topicHeinrich W. Guggenheimer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicdifferential geometry
- Category Latest Changes
- Started by Urs
- Comments 31
- Last comment by Urs
- Last Active 1 day ago

have expanded the single sentence at differential geometry to something like a paragraph, indicating how differential geometry is the “higher geometry modeled on the pre-geometry $\mathcal{G} = CartSp$”

- Discussion Type
- discussion topicsuper-embedding formalism
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 1 day ago

added pointer to Sorokin 01

- Discussion Type
- discussion topicRiemannian immersion
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 1 day ago

starting something on isometric immersions

— mainly I was trying to track down a reference that would clearly state that orthonormal “adapted” or “Darboux” (co)frames (here) always exist locally for an immersion into a Riemannian manifold.

What I found so far is

Mastrolia, Rigoli & Setti 2012, p. 33, where this is claimed, but just in passing

and

Chen & Giron 2021, Thm. 2.2, where this is stated in the generality of sequences of immersions, which makes it hard to recognize the simple statement behind all the analytic fine-print.

- Discussion Type
- discussion topicnegative type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 1 day ago

- Discussion Type
- discussion topiccartesian multicategory
- Category Latest Changes
- Started by Mike Shulman
- Comments 7
- Last comment by varkor
- Last Active 1 day ago

Created cartesian multicategory.

- Discussion Type
- discussion topicNarya
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by David_Corfield
- Last Active 1 day ago

- Discussion Type
- discussion topicequivalence type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Mike Shulman
- Last Active 1 day ago

starting page on the equivalence type, and moving some information on equivalence in type theory over to this page

Anonymous

- Discussion Type
- discussion topicone-to-one correspondence
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Mike Shulman
- Last Active 1 day ago

- Discussion Type
- discussion topicdefinitional isomorphism
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Mike Shulman
- Last Active 1 day ago

- Discussion Type
- discussion topicclosed monoidal category
- Category Latest Changes
- Started by Mike Shulman
- Comments 29
- Last comment by ncfavier
- Last Active 2 days ago

added to closed monoidal category a proof that the pointwise tensor product on a functor category with complete codomain is closed.

- Discussion Type
- discussion topicrecord type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topichigher observational type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 12
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicAleksandr A. Zheltukhin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicVladimir Tkach
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicinternal profunctor
- Category Latest Changes
- Started by FinnLawler
- Comments 17
- Last comment by BryceClarke
- Last Active 2 days ago

Created internal profunctor, which also describes an idea I saw somewhere about internal diagrams in fibrations over the base category. I added what I think are two examples, and asked a generic 'Help!' question. It might be better off on a page of its own, though.

- Discussion Type
- discussion topicElisabeth Stenholm
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by nLab edit announcer
- Last Active 2 days ago

Starting page for one of the authors of the publication

- Håkon Robbestad Gylterud, Elisabeth Bonnevier,
*Non-wellfounded sets in HoTT*(arXiv:2001.06696)

Anonymous

- Håkon Robbestad Gylterud, Elisabeth Bonnevier,

- Discussion Type
- discussion topicHåkon Robbestad Gylterud
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicmaterial set theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 41
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicweak type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicpolar coordinates
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by TobyBartels
- Last Active 2 days ago

- Discussion Type
- discussion topiccohomology of classifying spaces
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active 3 days ago

- Discussion Type
- discussion topicGram-Schmidt process
- Category Latest Changes
- Started by Todd_Trimble
- Comments 24
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicsubmanifold
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

added (here) statement of the existence of “slice charts” for submanifolds, with pointer to Lee 2012, Thm. 5.8

- Discussion Type
- discussion topicimmersion of smooth manifolds
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active 3 days ago

created

*immersion of smooth manifolds*.Stated also the definition that $f : X \to Y$ is an immersion precisely if the canonical morphism

$T X \to X \times_Y T Y =: f^* Y$is an injection.

This style of writing the conditon I have now also added to

*submersion*(where this canonical morphism is a surjection) and to*local diffeomorphism*(where it is an iso).This way of stating the condition makes most manifest that with respect to the infinitesimal cohesion $i :$ Smooth∞Grpd $\hookrightarrow$ SynthDiff∞Grpd we have

immersion $\Leftrightarrow$ formally unramified morphism

submersion $\Leftrightarrow$ formally smooth morphism

local diffeomorphism $\Leftrightarrow$ formally etale morphism

- Discussion Type
- discussion topicWilliam M. Boothby
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicLean
- Category Latest Changes
- Started by Urs
- Comments 54
- Last comment by perezl.alonso
- Last Active 3 days ago

added references to

*Lean*

- Discussion Type
- discussion topicenveloping von Neumann algebra
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 4 days ago

- Discussion Type
- discussion topicEric Berger
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicNathan Jacobson
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 4 days ago

- Discussion Type
- discussion topicdual gebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 4 days ago

- Discussion Type
- discussion topicmodels for concurrency
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicanti-Yetter-Drinfeld module
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

Starting splitting this topic off from growing related page Yetter-Drinfeld module.

- Discussion Type
- discussion topictransition system
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by nLab edit announcer
- Last Active 4 days ago

- Discussion Type
- discussion topicmonads of probability, measures, and valuations
- Category Latest Changes
- Started by PaoloPerrone
- Comments 9
- Last comment by nLab edit announcer
- Last Active 4 days ago

- Discussion Type
- discussion topicAtabey Kaygun
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 4 days ago

- Discussion Type
- discussion topicuniversal vector bundle
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Mark John Hopkins
- Last Active 4 days ago

- Discussion Type
- discussion topicYoneda lemma for (infinity,1)-categories
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by David_Corfield
- Last Active 4 days ago

For completeness I have added pointer to

- Emily Riehl, Dominic Verity, Section 6 of:
*Fibrations and Yoneda’s lemma in an $\infty$-cosmos*, Journal of Pure and Applied Algebra Volume 221, Issue 3, March 2017, Pages 499-564 (arXiv:1506.05500, doi:10.1016/j.jpaa.2016.07.003)

though there should really be some accompanying discussion of how this form of the statement is related to the usual one in terms of presheaves.

- Emily Riehl, Dominic Verity, Section 6 of:

- Discussion Type
- discussion topicelliptic genera as partition functions -- references
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active 4 days ago

a bare list of references, to be

`!include`

-ed into relevant entries (such as*Witten genus*,*M5-brane elliptic genus*but also inside*elliptic cohomology – references*) – for ease of harmonizing lists of references

- Discussion Type
- discussion topicD=5 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

quick note for

*5-dimensional Chern-Simons theory*, for the moment just to record some references

- Discussion Type
- discussion topicspan
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by varkor
- Last Active 4 days ago

Changes made only to the Universal property of the 2-category of spans section. The citations by Urs lead to another citation which, in turn, leads to another citation. With a little effort, I tracked down the a full copy of said universal property, I’ve replicated it here, added the citation used, although I left the previous citations there for convenience; a more experienced editor can remove those if they would like.

I would like to note that the author whose work I have referenced, Hermida, also notes: “[this universal property] is folklore although we know no references for it.”

Please make any corrections needed and clean up the language here; this is a fairly direct copy of what is written, but I imagine somebody with more knowledge of all the language used here can rewrite this universal property stuff in a cleaner way.

Thanks!

Anonymous

- Discussion Type
- discussion topicHopf-Galois extension
- Category Latest Changes
- Started by David_Corfield
- Comments 6
- Last comment by zskoda
- Last Active 5 days ago

Added a reference

- John Rognes,
*Galois extensions of structured ring spectra/Stably dualizable groups*, Memoires of the American Mathematical Society, 192(898), 2008, partly available as (pdf)

- John Rognes,

- Discussion Type
- discussion topicMorava K-theory
- Category Latest Changes
- Started by Jon Beardsley
- Comments 23
- Last comment by Urs
- Last Active 5 days ago

- Created a page Morava K-theory . A lot to add. Will fill out later, with better reference list. Please edit!

- Discussion Type
- discussion topicSchneider's theorem
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 5 days ago

- Discussion Type
- discussion topicHans-Jürgen Schneider
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 5 days ago

- Discussion Type
- discussion topicclassifying space
- Category Latest Changes
- Started by Urs
- Comments 45
- Last comment by Urs
- Last Active 5 days ago

I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.

I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.

In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes

- Discussion Type
- discussion topicconfiguration space of points
- Category Latest Changes
- Started by Tim_Porter
- Comments 102
- Last comment by Urs
- Last Active 5 days ago

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

- Discussion Type
- discussion topicHopf module
- Category Latest Changes
- Started by perezl.alonso
- Comments 2
- Last comment by zskoda
- Last Active 5 days ago

expanded a bit on the Fundamental theorem of Hopf modules, added reference

- Joost Vercruysse.
*Hopf algebras—Variant notions and reconstruction theorems*. (2012). (arXiv:1202.3613)

- Joost Vercruysse.