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- Discussion Type
- discussion topicKan fibration
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Apr 20th 2023

added the pointers to the combinatorial proofs of the fiberwise detection of acyclicity of Kan fibrations, currently discussed on the AlgTop list, to the nLab here.

- Discussion Type
- discussion topicIntroduction to Homotopy Theory
- Category Latest Changes
- Started by Oscar_Cunningham
- Comments 5
- Last comment by nLab edit announcer
- Last Active Apr 20th 2023

- Discussion Type
- discussion topicDold-Kan correspondence
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by Urs
- Last Active Apr 20th 2023

added reference to dendroidal version of Dold-Kan correspondence

- Discussion Type
- discussion topicvertex operator algebra
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by zskoda
- Last Active Apr 20th 2023

I have expanded vertex operator algebra (more references, more items in the Properties-section) in partial support to a TP.SE answer that I posted here

- Discussion Type
- discussion topicdagger category
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by varkor
- Last Active Apr 20th 2023

I took the liberty of incorporating material from Andre Joyal's latest message to the CatTheory mailing list into the entry dagger-category:

created sections

- Discussion Type
- discussion topicCenter for Quantum and Topological Systems
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Apr 20th 2023

- Discussion Type
- discussion topicconnective spectrum
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 20th 2023

cross-linked with

*t-structure*(here)

- Discussion Type
- discussion topicconnective chain complex
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Apr 20th 2023

the entry

*Dold-Kan correspondence*and several related entries had long been asking for*connective chain complex*. I have now started something there. Of course this can be much further expanded on…

- Discussion Type
- discussion topicconnective
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 20th 2023

- Discussion Type
- discussion topicn-connective object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 20th 2023

a small entry to make room for the notion of $n$-connectivity with respect to t-structures, to cross-link entries such as

*connective chain complex*and*connective spectra*, and to disambiguate from “$n$-connected object”.

- Discussion Type
- discussion topicn-connected object of an (infinity,1)-topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 20th 2023

I am removing all redirects for “connective” from this entry, in order to make room for a dedicated entry “n-connective object” which makes room for disambiguation with the notion of connectivity in stable $\infty$-categories with t-structure.

- Discussion Type
- discussion topicstring-localized quantum field
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 20th 2023

added pointer to today’s:

- Christian Gaß, José M. Gracia-Bondía, Karl-Henning Rehren,
*Quantum general covariance*[arXiv:2304.09843]

- Christian Gaß, José M. Gracia-Bondía, Karl-Henning Rehren,

- Discussion Type
- discussion topicAndrews–Curtis conjecture
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicNullstellensatz
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by John Baez
- Last Active Apr 19th 2023

wrote something at

*Nullstellensatz*, prompted by this old MO comment by Lawvere.

- Discussion Type
- discussion topicRichard J. Wood
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicadjoint string
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topictotally distributive category
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicdistributive category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 29
- Last comment by David_Corfield
- Last Active Apr 19th 2023

Spurred by an MO discussion, I added the observation that coproduct inclusions are monic in a distributive category.

- Discussion Type
- discussion topicdoubly closed monoidal category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicmonoidal topos
- Category Latest Changes
- Started by spitters
- Comments 3
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topiccosmic inflation
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Apr 19th 2023

stub for

*cosmic inflation*(for the moment just to record some references)

- Discussion Type
- discussion topicStable categories and structured ring spectra
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicdg-category
- Category Latest Changes
- Started by adeelkh
- Comments 15
- Last comment by Tim_Porter
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicAlexei Bondal
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Apr 19th 2023

- Discussion Type
- discussion topicrational vertex operator algebra
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by Urs
- Last Active Apr 18th 2023

- Discussion Type
- discussion topicModel Categories
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Apr 18th 2023

I am giving Hovey’s book a

`category:reference`

-entry, as demanded by Dmitri in*pointed model category*

- Discussion Type
- discussion topicKoszul duality
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by zskoda
- Last Active Apr 18th 2023

Added

- Jonathan Beardsley, Maximilien Péroux,
*Koszul Duality in Higher Topoi*, (arXiv:1909.11724)

- Jonathan Beardsley, Maximilien Péroux,

- Discussion Type
- discussion topicsymmetry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Guest
- Last Active Apr 18th 2023

added pointer to:

- Marc Bezem, Ulrik Buchholtz, Pierre Cagne, Bjørn Ian Dundas, Daniel R. Grayson:
*Symmetry*(2021) $[$pdf$]$

- Marc Bezem, Ulrik Buchholtz, Pierre Cagne, Bjørn Ian Dundas, Daniel R. Grayson:

- Discussion Type
- discussion topiccategory of chain complexes
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 18th 2023

I have polished

*category of chain complexes*a little more and started a section (but unfinished) with discussion of that and how $Ch_\bullet(\mathcal{A})$ is itself again an abelian category

- Discussion Type
- discussion topicsimplicial loop space
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 18th 2023

added pointer to

- Danny Stevenson,
*Décalage and Kan’s simplicial loop group functor*, Theory and Applications of Categories, Vol. 26, 2012, No. 28, pp 768-787 (arXiv:1112.0474, tac:26-28)

- Danny Stevenson,

- Discussion Type
- discussion topicKumar S. Gupta
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active Apr 18th 2023

- Discussion Type
- discussion topictopological phase of matter
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active Apr 18th 2023

added these pointers on classification of topological phases of matter via tensor network states:

C. Wille, O. Buerschaper, Jens Eisert,

*Fermionic topological quantum states as tensor networks*, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)Andreas Bauer, Jens Eisert, Carolin Wille,

*Towards a mathematical formalism for classifying phases of matter*(arXiv:1903.05413)

- Discussion Type
- discussion topiccomprehensive factorization system
- Category Latest Changes
- Started by Joshua Meyers
- Comments 19
- Last comment by BryceClarke
- Last Active Apr 18th 2023

Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor

Todo: add more proofs of this result.

For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:

An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out

How can I fix this?

- Discussion Type
- discussion topicGrothendieck category
- Category Latest Changes
- Started by zskoda
- Comments 18
- Last comment by Urs
- Last Active Apr 18th 2023

I strongly disagree with the statement in Grothendieck category that the Grothendieck category is small. The main examples like ${}_R Mod$ are not! What did the writer of that line have in mind ?

- Discussion Type
- discussion topicBekenstein-Hawking entropy
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Apr 18th 2023

added pointer, here and in related entries, to

- Gary Gibbons, Malcolm J. Perry,
*Black Holes and Thermal Green Functions*, Vol. 358, No. 1695 (1978) (jstor:79482)

being one of the early references considering the computation of black hole radiation in terms of thermal field theory on Wick-rotated spacetimes with compact/periodic “Euclidean time”.

- Gary Gibbons, Malcolm J. Perry,

- Discussion Type
- discussion topicSchwinger effect
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Apr 18th 2023

- Discussion Type
- discussion topicMarco Chiodaroli
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 18th 2023

- Discussion Type
- discussion topicHenrik Johansson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 18th 2023

- Discussion Type
- discussion topicJohn Joseph Carrasco
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 18th 2023

- Discussion Type
- discussion topicKLT relations
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Apr 18th 2023

at

*KLT relations*I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).In this course I also expanded the list of references at quantum gravity – As a perturbative quantum field theory

- Discussion Type
- discussion topiclattice (discrete subgroup)
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Apr 18th 2023

found this article as well, going to merge lattice (in a vector space, etc.) into here

Anonymous

- Discussion Type
- discussion topicoidification - table
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by maxsnew
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicmodel structure for parameterized spectra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicmixed motive
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2023

added pointer to:

- Denis-Charles Cisinski, Frédéric Déglise,
*Triangulated categories of mixed motives*, Springer Monographs in Mathematics, Springer (2019) [arXiv:0912.2110, doi:10.1007/978-3-030-33242-6]

and publication data for:

- Denis-Charles Cisinski, Frédéric Déglise,
*Local and stable homological algebra in Grothendieck abelian categories*, Homology, Homotopy and Applications**11**1 (2009) 219–260 [arXiv:0712.3296, hha:1251832567]

- Denis-Charles Cisinski, Frédéric Déglise,

- Discussion Type
- discussion topicMichael Roy
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicAufhebung
- Category Latest Changes
- Started by Urs
- Comments 77
- Last comment by Thomas Holder
- Last Active Apr 17th 2023

Thomas Holder has been working on

*Aufhebung*. I have edited the formatting a little (added hyperlinks and more Definition-environments, added another subsection header and some more cross-references, cross-linked with*duality of opposites*).

- Discussion Type
- discussion topicNewman's lemma
- Category Latest Changes
- Started by J-B Vienney
- Comments 8
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicNewman's diamond lemma > history
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by Urs
- Last Active Apr 17th 2023

Stub, redirects Newman’s theorem.

- Discussion Type
- discussion topicknots-quivers correspondence
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicMathematica
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2023

added pointer to the landing page (www.wolfram.com/mathematica) and cross-link with

*Stephen Wolfram*

- Discussion Type
- discussion topicStephen Wolfram
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicmachine learning
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topicn-excisive functor
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active Apr 17th 2023

added to

*n-excisive functor*a section

- Discussion Type
- discussion topicVectBund
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 17th 2023

starting a dedicated entry for the category of vector bundles with homomorphisms allowed to cover non-trivial base maps (while previously we only had VectBund(B) for fixed base $B$).

For the moment the main point is to record the interesting cartesian- and tensor-monoidal structure (now here)

- Discussion Type
- discussion topicbundles - contents
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Apr 17th 2023

I found it was time to have a general table of contents

*bundles - contents*to be added as a floating table to the relevant entries. So I started one.

- Discussion Type
- discussion topicsemi-simplicial set
- Category Latest Changes
- Started by Mike Shulman
- Comments 22
- Last comment by Thomas Holder
- Last Active Apr 17th 2023

Created semi-simplicial set, mainly as a repository for some terminological remarks. I would welcome anyone more knowledgeable about the history to correct or improve it!

- Discussion Type
- discussion topicstringor bundle
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 17th 2023

- Discussion Type
- discussion topiczero bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2023

a fairly trivial entry, for the purpose of easing the hyperlinking in entries like

*bireflective subcategory*,*parameterized spectra*,*VectBund*, etc.

- Discussion Type
- discussion topicexcisive (∞,1)-functor
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Urs
- Last Active Apr 17th 2023

Added the reference now that it has appeared:

- {#AnelBiedermanFinsterJoyal17b} Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal,
*Goodwillie’s Calculus of Functors and Higher Topos Theory*(arXiv:1703.09632)

- {#AnelBiedermanFinsterJoyal17b} Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal,

- Discussion Type
- discussion topicJeroen Hekking
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 17th 2023