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- Discussion Type
- discussion topicYong-Geun Oh
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 2nd 2024

Added selected writing from other pages (and also linked Yong-Geun Oh there when necessary).

- Discussion Type
- discussion topicsymplectic topology
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 2nd 2024

- Discussion Type
- discussion topicadjoint functor
- Category Latest Changes
- Started by Urs
- Comments 79
- Last comment by nLab edit announcer
- Last Active Jun 2nd 2024

added at adjoint functor

more details in the section In terms of universal arrows;

a bit in the section Examples

- Discussion Type
- discussion topicZbigniew Semadeni
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 2nd 2024

- Discussion Type
- discussion topicMikhail Gromov
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jun 2nd 2024

Added paper on Alexandrov spaces with new link to a pdf.

- Discussion Type
- discussion topicsketch
- Category Latest Changes
- Started by David_Corfield
- Comments 23
- Last comment by Urs
- Last Active Jun 2nd 2024

I pasted in something Mike wrote on sketches and accessible models to sketch. But now it needs tidying up, and I’m wondering if it might have been better placed at accessible category. Alternatively we start a new page on sketch-theoretic model theory. Ideas?

- Discussion Type
- discussion topicYuri Burago
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 2nd 2024

- Discussion Type
- discussion topicAlexandrov space
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Jun 2nd 2024

am adding references to Alexandrov space

- Discussion Type
- discussion topicGrigori Perelman
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 2nd 2024

Added four selected works, including the central part of the proof of the Poincaré conjecture.

- Discussion Type
- discussion topicmetacompact space
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jun 2nd 2024

- Discussion Type
- discussion topicinverter
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active Jun 1st 2024

Explicitly mention that inverters are representably fully faithful.

- Discussion Type
- discussion topictype theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 103
- Last comment by nLab edit announcer
- Last Active Jun 1st 2024

I incorporated some of my spiel from the blog into the page type theory.

- Discussion Type
- discussion topicYoshiki Kinoshita
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 1st 2024

- Discussion Type
- discussion topicopposite category
- Category Latest Changes
- Started by John Baez
- Comments 14
- Last comment by Urs
- Last Active Jun 1st 2024

I made a little addition to opposite category, pointing out some amusing nuances regarding the opposite of a $V$-enriched category when $V$ is merely braided. This remark could surely be clarified, but I think you’ll get the idea.

(In case you’re wondering why I did this, it’s because I needed a reference for “opposite category” in a blog entry I’m writing.)

- Discussion Type
- discussion topicprincipal ideal domain
- Category Latest Changes
- Started by Todd_Trimble
- Comments 15
- Last comment by RodMcGuire
- Last Active Jun 1st 2024

More examples added at principal ideal domain.

- Discussion Type
- discussion topicfirst-countable space
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 2
- Last comment by Urs
- Last Active Jun 1st 2024

- Discussion Type
- discussion topiclocally compact topological space
- Category Latest Changes
- Started by Urs
- Comments 66
- Last comment by Urs
- Last Active Jun 1st 2024

I gave

*locally compact topological space*an Idea-section and added the other equivalent definition (here).

- Discussion Type
- discussion topicArens-Fort space
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 1st 2024

Created page for Arens-Fort space with properties taken from the english Wikipedia page.

- Discussion Type
- discussion topicsecond-countable space
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 1st 2024

- Discussion Type
- discussion topicAnton A. Burkov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 31st 2024

- Discussion Type
- discussion topicsemi-metal
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active May 31st 2024

- Discussion Type
- discussion topicspin^h structure
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 9
- Last comment by Dmitri Pavlov
- Last Active May 31st 2024

- Discussion Type
- discussion topicNambu-Goto action
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 31st 2024

finally added the original references

Yoichiro Nambu,

*Duality and Hadrodynamics*, Notes prepared for the Copenhagen High Energy Symposium (1970) [doi:10.1142/9789812795823_0026]Tetsuo Gotō,

*Relativistic Quantum Mechanics of One-Dimensional Mechanical Continuum and Subsidiary Condition of Dual Resonance Model*, Progress of Theoretical Physics**46**5 (1971) 1560–1569 [doi:10.1143/PTP.46.1560]

- Discussion Type
- discussion topicrational homology sphere
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active May 31st 2024

Created bare minimum for rational homology sphere, which will be expanded later.

- Discussion Type
- discussion topichomology sphere
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active May 31st 2024

- Discussion Type
- discussion topicThors Hans Hansson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 31st 2024

- Discussion Type
- discussion topicfree coproduct completion
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by BryceClarke
- Last Active May 31st 2024

some bare minimum on the free coproduct cocompletion.

The term used to redirect to the entry

*free cartesian category*, where however the simple idea of free coproduct completion wasn’t really brought out.

- Discussion Type
- discussion topicFelix von Oppen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 31st 2024

- Discussion Type
- discussion topic6j symbol
- Category Latest Changes
- Started by Milo Moses
- Comments 2
- Last comment by perezl.alonso
- Last Active May 31st 2024

- Discussion Type
- discussion topicsmooth manifold
- Category Latest Changes
- Started by Urs
- Comments 49
- Last comment by Urs
- Last Active May 31st 2024

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 $\mathcal{G} = CartSp$-schemes).

- Discussion Type
- discussion topiclinear logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 42
- Last comment by Urs
- Last Active May 31st 2024

The cut rule for linear logic used to be stated as

If $\Gamma \vdash A$ and $A \vdash \Delta$, then $\Gamma \vdash \Delta$.

I don’t think this is general enough, so I corrected it to

If $\Gamma \vdash A, \Phi$ and $\Psi,A \vdash \Delta$, then $\Psi,\Gamma \vdash \Delta,\Phi$.

- Discussion Type
- discussion topicstring field theory
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active May 31st 2024

I have started adding references to

*string field theory*, in particular those by Jim Stasheff et al. on the role of L-infinity algebra and A-infinity algebra. Maybe I find time later to add more details.

- Discussion Type
- discussion topicelliptic genera as partition functions -- references
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active May 31st 2024

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 topicball
- Category Latest Changes
- Started by Urs
- Comments 57
- Last comment by Dmitri Pavlov
- Last Active May 31st 2024

created ball

- Discussion Type
- discussion topicAb-enriched category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by RodMcGuire
- Last Active May 30th 2024

- Discussion Type
- discussion topicopetope
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active May 30th 2024

some trivial edits to opetope (a toc, some hyperlinks)

- Discussion Type
- discussion topicMichel Demazure
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active May 30th 2024

Functor of points approach to algebraic schemes and algebraic groups is in

- Michel Demazure, Pierre Gabriel,
*Groupes algebriques*, tome 1 (later volumes never appeared), Mason and Cie, Paris 1970; engl. translation Michel Demazure, Peter Gabriel,*Introduction to algebraic geometry and algebraic groups*, North-Holland mathematics studies 39

- Michel Demazure, Pierre Gabriel,

- Discussion Type
- discussion topicOre localization
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 30th 2024

- Discussion Type
- discussion topicGabriel localization
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 30th 2024

- Pierre Gabriel,
*La localisation dans les anneaux non commutatifs*, Séminaire Dubreil (1959-1960), exposé 2, 1–35 numdam:pdf - A. L. Rosenberg,
*Non-commutative affine semischemes and schemes*, Seminar on supermanifolds**26**, Dept. Math., U. Stockholm (1988) pdf

- Pierre Gabriel,

- Discussion Type
- discussion topicaffine scheme
- Category Latest Changes
- Started by IngoBlechschmidt
- Comments 12
- Last comment by zskoda
- Last Active May 30th 2024

At

*affine scheme*, the fundamental theorem on morphisms of schemes was stated the other way round. I fixed that.As a handy mnemonic, here is a quick and down-to-earth way to see that the claim “$Sch(Spec R, Y) \cong CRing(\mathcal{O}_Y(Y), R)$” is wrong. Take $Y = \mathbb{P}^n$ and $R = \mathbb{Z}$. Then the left hand side consists of all the $\mathbb{Z}$-valued points of $\mathbb{P}^n$. On the other hand, the right hand side only contains the unique ring homomorphism $\mathbb{Z} \to \mathbb{Z}$, since $\mathcal{O}_{\mathbb{P}^n}(\mathbb{P}^n) \cong \mathbb{Z}$.

- Discussion Type
- discussion topicGaussian elimination
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active May 30th 2024

- Discussion Type
- discussion topicYa-Wen Sun
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 30th 2024

- Discussion Type
- discussion topicquantum computation
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by Urs
- Last Active May 30th 2024

stub for

*quantum computation*

- Discussion Type
- discussion topicsession type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active May 30th 2024

- Discussion Type
- discussion topicMichel H. Devoret
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 29th 2024

- Discussion Type
- discussion topicOlivier Ezratty
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 29th 2024

- Discussion Type
- discussion topicsuperconducting qbits -- references
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 29th 2024

a bare list of references, to be

`!include`

-ed into the References-section of relevant entries (such as at*superconductivity*,*qbit*,*quantum computation*and maybe*Josephson junction*), for ease of synchronizingWhat I am still looking for is an expository reference which would very clearly say that quantum gates in these architectures

*are electromagnetic pulses*, so that quantum circuits are pulse protocols. This is so obvious to all the experts that they tend to forget to say it when explaining the basics…

- Discussion Type
- discussion topicsuplattice
- Category Latest Changes
- Started by John Baez
- Comments 13
- Last comment by RodMcGuire
- Last Active May 29th 2024

- Discussion Type
- discussion topicparafermion
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active May 29th 2024

- Discussion Type
- discussion topicPolish space
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Urs
- Last Active May 29th 2024

- Started here.

- Discussion Type
- discussion topicCP violation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 29th 2024

added pointer to:

Wen-Yuan Ai, Juan S. Cruz, Bjorn Garbrecht, Carlos Tamarit,

*Absence of CP violation in the strong interactions*[arXiv:2001.07152]published as:

*Consequences of the order of the limit of infinite spacetime volume and the sum over topological sectors for C P violation in the strong interactions*Phys. Lett. B**822**(2021) 136616 [doi:10.1016/j.physletb.2021.136616]Wen-Yuan Ai, Bjorn Garbrecht, Carlos Tamarit,

*CP conservation in the strong interactions*, Universe**10**5 (2024) 189 [arXiv:2404.16026, doi:10.3390/universe10050189]

- Discussion Type
- discussion topicaccessible (infinity,1)-functor
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active May 29th 2024

- Discussion Type
- discussion topicÉvariste Galois
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active May 28th 2024

- Discussion Type
- discussion topiccoimage
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by nLab edit announcer
- Last Active May 28th 2024

- Discussion Type
- discussion topicSanath Devalapurkar
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active May 28th 2024

- Discussion Type
- discussion topicEd Segal
- Category Latest Changes
- Started by perezl.alonso
- Comments 1
- Last comment by perezl.alonso
- Last Active May 28th 2024

- Discussion Type
- discussion topicmatrix factorization
- Category Latest Changes
- Started by Kevin Lin
- Comments 9
- Last comment by perezl.alonso
- Last Active May 28th 2024

- Added a page on matrix factorizations.

- Discussion Type
- discussion topicarithmetic pretopos
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by John Baez
- Last Active May 28th 2024

stub for

*arithmetic pretopos*, just to record the reference

- Discussion Type
- discussion topicPROP
- Category Latest Changes
- Started by fpaugam
- Comments 34
- Last comment by Urs
- Last Active May 28th 2024

- I would like to include something on wheeled properads (or wheeled PROPs) in the nlab. It seems to me that a wheeled prop is something like a symmetric monoidal category with duals for every object generated by one object. Is this right? Is there a place in the litterature where i can find the relation between wheeled properads used by Merkulov and some kinds of symmetric monoidal categories with duality?

Before changing the PROP entry to add this variant, i would like to have a nice reference on this.

- Discussion Type
- discussion topicanyonic braiding in momentum space -- references
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active May 28th 2024

a bare list of references, to be

`!include`

-ed into the References-section of relevant entries (such as at*braid group representation*and at*semi-metal*).Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited