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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topicconvex space
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by John Baez
- Last Active 7 hours ago

Added cross-link with

*convex function*.Also hyperlinked various keywords as well as some author names in the list of references.

- Discussion Type
- discussion topiccomplex analysis
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active 9 hours ago

New entry complex analysis.

- Discussion Type
- discussion topicnumber
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Urs
- Last Active 11 hours ago

- Discussion Type
- discussion topicCantor cube
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 12 hours ago

- Discussion Type
- discussion topicdyadic space
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 12 hours ago

- Discussion Type
- discussion topicKiyoshi Igusa
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 13 hours ago

- Discussion Type
- discussion topicfibration of points
- Category Latest Changes
- Started by BryceClarke
- Comments 5
- Last comment by Urs
- Last Active 13 hours ago

Added (what I believe to be is) the original reference:

- Dominique Bourn,
*Normalization equivalence, kernel equivalence and affine categories*, Lecture Notes in Mathematics,**1488**, 1991. (doi:10.1007/BFb0084212)

I’m leaving a note here to add more to this page relating to Malcev categories and protomodular categories.

- Dominique Bourn,

- Discussion Type
- discussion topicautomorphic form
- Category Latest Changes
- Started by Urs
- Comments 35
- Last comment by nLab edit announcer
- Last Active 14 hours ago

stub for

*automorphic form*,to go with the blog discussion here

- Discussion Type
- discussion topiclocalization of a ring
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by zskoda
- Last Active 15 hours ago

created

*localization of a ring*

- Discussion Type
- discussion topicright-connected double category
- Category Latest Changes
- Started by BryceClarke
- Comments 9
- Last comment by BryceClarke
- Last Active 16 hours ago

- Discussion Type
- discussion topiccosine
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active 17 hours ago

- Discussion Type
- discussion topicsine
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 17 hours ago

- Discussion Type
- discussion topicexponential map
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 17 hours ago

- Discussion Type
- discussion topicconstructive analysis
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 18 hours ago

added some references on

*constructive analysis*here.

- Discussion Type
- discussion topicalgebraic weak factorization system
- Category Latest Changes
- Started by BryceClarke
- Comments 2
- Last comment by BryceClarke
- Last Active 18 hours ago

- Discussion Type
- discussion topicRobbert Krebbers
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 18 hours ago

- Discussion Type
- discussion topicL.E.J. Brouwer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 18 hours ago

- Discussion Type
- discussion topicconstructive mathematics
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 19 hours ago

I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to

- Discussion Type
- discussion topicrational number
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 7
- Last comment by Urs
- Last Active 19 hours ago

- Discussion Type
- discussion topicinteger
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active 19 hours ago

noticed that the entry was missing, so I created a stub for integer

- Discussion Type
- discussion topic1lab
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 19 hours ago

- Discussion Type
- discussion topictabulator
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by Urs
- Last Active 20 hours ago

- Discussion Type
- discussion topicexistential quantifier
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 20 hours ago

I have tried to brush-up

*existential quantifier*a little more. But not really happy with it yet.

- Discussion Type
- discussion topicbeing
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active 1 day ago

added link to existential quantifier

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

- Discussion Type
- discussion topicsetoid
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by Urs
- Last Active 1 day ago

Created a stub / disambiguation page, to point to both equivalence relation and Bishop set and pseudo-equivalence relation (the latter currently redirecting to regular and exact completions).

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

- Discussion Type
- discussion topicquotient type
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active 1 day ago

I notice that there seemed to be no-where a really explicit semantics explanation of the claim that “univalence implies the existence of quotient types”. I checked with Peter Lumsdaine, and he kindly provided some text which, up to some minor reformatting, I have put into quotient type – Properties – from univalence.

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

added publication data to

- Egbert Rijke, Bas Spitters,
*Sets in homotopy type theory*, Mathematical Structures in Computer Science**25**5 “From type theory and homotopy theory to Univalent Foundations of Mathematics” (2015) 1172-1202 [doi:10.1017/S0960129514000553, arXiv:1305.3835]

here and elsewhere

- Egbert Rijke, Bas Spitters,

- Discussion Type
- discussion topicnatural number
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by Urs
- Last Active 1 day ago

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

I looked at

*real number*and thought I could maybe try to improve the way the Idea section flows. Now it reads as follows:A

*real number*is something that may be approximated by rational numbers. Equipped with the operations of addition and multiplication induced from the rational numbers, real numbers form a*number field*, denoted $\mathbb{R}$. The underlying set is the*completion*of the ordered field $\mathbb{Q}$ of rational numbers: the result of adjoining to $\mathbb{Q}$ suprema for every bounded subset with respect to the natural ordering of rational numbers.The set of real numbers also carries naturally the structure of a topological space and as such $\mathbb{R}$ is called the

*real line*also known as*the continuum*. Equipped with both the topology and the field structure, $\mathbb{R}$ is a topological field and as such is the uniform completion of $\mathbb{Q}$ equipped with the absolute value metric.Together with its cartesian products – the Cartesian spaces $\mathbb{R}^n$ for natural numbers $n \in \mathbb{N}$ – the real line $\mathbb{R}$ is a standard formalization of the idea of

*continuous space*. The more general concept of (smooth)*manifold*is modeled on these Cartesian spaces. These, in turnm are standard models for the notion of space in particular in physics (see*spacetime*), or at least in classical physics. See at*geometry of physics*for more on this.

- Discussion Type
- discussion topicoperad
- Category Latest Changes
- Started by Todd_Trimble
- Comments 19
- Last comment by anuyts
- Last Active 1 day ago

Wrote a section on the associated monad at operad, in terms of the framework introduced under the section titled Preparation.

- Discussion Type
- discussion topichorizontal categorification
- Category Latest Changes
- Started by Evan Patterson
- Comments 8
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicgroup of units
- Category Latest Changes
- Started by Todd_Trimble
- Comments 6
- Last comment by Urs
- Last Active 1 day ago

Generalized the definition at group of units, and added another example (analyzing the group of units of the $p$-adic integers).

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

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

touched the formatting in

*congruence*, fixed a typo on the cartesian square, added a basic example

- Discussion Type
- discussion topicalgebra
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 1 day ago

the topic-cluster “algebra” is stiil a little orphaned on the Lab, I find. I added a bit to

but these entries are still a bit pitiful. Maybe somebody feels challenged to turn them into good entries. Especially the latter.

Should we have pages algebra over a Lawvere theory, algebra over a PROP, etc? Some entries look like they want such links (for instance algebra itself).

- Discussion Type
- discussion topicgroup theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 1 day ago

added pointer to:

Eugene P. Wigner

*Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren*, Springer (1931) [doi:10.1007/978-3-663-02555-9, pdf]Eugene P. Wigner,

*Group theory: And its application to the quantum mechanics of atomic spectra*, 5, Academic Press (1959) [doi:978-0-12-750550-3]

- Discussion Type
- discussion topicSymmetry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 1 day ago

am giving unimath.github.io/SymmetryBook/book.pdf a

`category:reference`

-entry

- Discussion Type
- discussion topiclocalization of a commutative ring
- Category Latest Changes
- Started by Richard Williamson
- Comments 2
- Last comment by Urs
- Last Active 1 day ago

As promised, tweaked the example of inverting a single element, to point instead to localisation of a commutative ring at an element.

- Discussion Type
- discussion topicseparator
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by nLab edit announcer
- Last Active 2 days ago

I created

*separator*, while having the nagging feeling that we already have this entry. Of course after creating it I remembered the page*generator*.So we should merge the stuff. Might this be an occasion to merge

*away*from*generator*? A set of “generating objects” also means other things than “separating objects” (notably colimit generation). So I’d be inclined to move all material to*separator*. That would also allow to drop the warning at the beginning of*generator*.

- Discussion Type
- discussion topicVladimir Vapnik
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by David_Corfield
- Last Active 2 days ago

- Discussion Type
- discussion topicsingular learning theory
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by David_Corfield
- Last Active 2 days ago

- Discussion Type
- discussion topicstring-net model
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicinclusion-exclusion
- Category Latest Changes
- Started by J-B Vienney
- Comments 2
- Last comment by nLab edit announcer
- Last Active 3 days ago

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

- Discussion Type
- discussion topicexcluded middle
- Category Latest Changes
- Started by Mike Shulman
- Comments 14
- Last comment by nLab edit announcer
- Last Active 3 days ago

I added to excluded middle a discussion of the constructive proof of double-negated LEM and how it is a sort of “continuation-passing” transform.

- Discussion Type
- discussion topicJennifer C. H. Wilson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicbraid group
- Category Latest Changes
- Started by Urs
- Comments 33
- Last comment by Urs
- Last Active 3 days ago

the entry

*braid group*said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).

- Discussion Type
- discussion topicmulti-adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 16
- Last comment by maxsnew
- Last Active 3 days ago

- Discussion Type
- discussion topicparametric right adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 17
- Last comment by maxsnew
- Last Active 3 days ago

Added alternative terminology “local right adjoint” and “strongly cartesian monad” from Berger-Mellies-Weber. They claim the former “has become the more accepted terminology” than “parametric right adjoint”; does anyone know other references to support this? (I think it’s certainly more logical, in that it fits with the general principle of “local” meaning “on slice categories” — not to be confused with the different general principle of “local” meaning “in hom-objects”.)

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

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

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

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

- Discussion Type
- discussion topicbundle gerbe module
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 3 days ago

I have added pointer to

- Ernesto Lupercio, Bernardo Uribe, Section 7.2 of:
*Gerbes over Orbifolds and Twisted K-theory*, Comm. Math. Phys. 245(3): 449-489. (arXiv:math/0105039, doi:10.1007/s00220-003-1035-x)

Their Prop. 7.2.2 is verbatim the characterization that BCMMS made the definition of “bundle gerbe module” a month and a half later (except that LU focus on open covers instead of more general surjective submersions, but that’s not an actual restriction and in any case not the core of the definition).

Also added pointer to

- Marco Mackaay,
*A note on the holonomy of connections in twisted bundles*, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 1, pp. 39-62. (arXiv:math/0106019, numdam:CTGDC_2003__44_1_39_0)

which essentially recovers Lupercio & Uribe’s Def. 7.2.1.

From the arXiv timestamps I gather that it must have been an intense couple of weeks for all these auhtors in spring 2001. But Lupercio & Uribe came out first, by a fair margin. And in equivariant generality, right away…

- Ernesto Lupercio, Bernardo Uribe, Section 7.2 of:

- Discussion Type
- discussion topicbiproduct
- Category Latest Changes
- Started by Colin Tan
- Comments 21
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicSpecht module
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by J-B Vienney
- Last Active 3 days ago

discovered this old stub entry, touched the wording, added some formatting, and pointer to:

- Bruce Sagan, Section 2.3 in:
*The symmetric group*, Springer 2001 (doi:10.1007/978-1-4757-6804-6, pdf)

- Bruce Sagan, Section 2.3 in:

- Discussion Type
- discussion topicGalois' last letter
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicgroup
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active 3 days ago

reformatted the entry group a little, expanded the Examples-section a little and then pasted in the group-related “counterexamples” from counterexamples in algebra. Mainly to indicate how I think this latter entry should eventually be used to improve the entries that it refers to.