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- Discussion Type
- discussion topicdivisible group
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Sep 27th 2012

stub for divisible group

- Discussion Type
- discussion topicinjective module
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 27th 2012

I have been adding basic propositons and their (farily) detailed proofs at

*injective object*in the section*Existence of enough injectives*.This expands on statements and proofs mentioned in other entries, notably at

*injective object*, also at*coextension of scalars*(stuff added by Todd, I think).Generally, it is often hard to decide in which entry exactly to put a theorem. Often there are several choices. Best of course to copy stuff to each relevant point or at least link to it from there.

But I am quite a bit time pressured now (and I hope that does not already show too much in what I just typed). So I won’t do any further such organization right now. But if anyone feels like looking into this, please don’t hesitate.

- Discussion Type
- discussion topictelescope conjecture
- Category Latest Changes
- Started by Jon Beardsley
- Comments 1
- Last comment by Jon Beardsley
- Last Active Sep 27th 2012

Created the page telescope conjecture since I noticed it was linked to by Morava K-theory but didn’t exist. Might add more later, specifically about how this is generalized to the setting of axiomatic stable homotopy categories and how it is true after localizing at $BP$, $E(n)$ and some other spectra, but believed to be false in general.

- Discussion Type
- discussion topicautomorphism infinity-group
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Sep 27th 2012

Since I was being asked I briefly expanded

*automorphism infinity-group*by adding the internal version and the HoTT syntax.Mike, what’s the best type theory syntax for the definition of $\mathbf{Aut}(X)$ via $\infty$-image factorization of the name of $X$?

- Discussion Type
- discussion topichypothesis and conclusion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 26th 2012

I made

*hypothesis*and*conclusion*entries or redirects to make*deduction and induction - contents*look nicer(Gee, and I was really just editing

*injective module*when the detour through Zorn’s lemma made me get distracted again by all this foundational business…)

- Discussion Type
- discussion topiccomposition
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 26th 2012

added to composition a new section with trivial remarks on composition in enriched category theory.

- Discussion Type
- discussion topicequivalence in homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 25th 2012

I had set out to add to the entry

*equivalence in homotopy type theory*a detailed derivation of the categorical semantics of $Equiv(X,Y)$. But then I ended up getting distracted by various editorial work in other entries and for the moment I only have this puny remark added, expanding on the previous discussion there.Maybe more later…

- Discussion Type
- discussion topicevaluation map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 25th 2012

I have slightly touched the paragraph

*Syntax and semantics*at*evaluation map*.And then I added to the entry

*internal hom*a similar Propeties-section*internal hom - Evaluation map*

- Discussion Type
- discussion topicThe Geometry of Physics - An Introduction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 25th 2012

I have started creating a hyperlinked index at

- Theodore Frankel,
*The Geometry of Physics - An Introduction*

A colleague may use this for a course and maybe we get a chance to polish and/or write up some more related material in relevant $n$Lab entries.

- Theodore Frankel,

- Discussion Type
- discussion topicgeometric point
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Tim_Porter
- Last Active Sep 25th 2012

created stubby geometric point

- Discussion Type
- discussion topicgeometric fibre
- Category Latest Changes
- Started by Tim_Porter
- Comments 14
- Last comment by Tim_Porter
- Last Active Sep 25th 2012

created geometric fibre. Can someone lease check these algebraic geometry entries as that area is quite far from my safety zone! so I will get some things wrong.

- Discussion Type
- discussion topicAndreas Blass
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Sep 25th 2012

created a stub Andreas Blass.

- Discussion Type
- discussion topicLévy hierarchy
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by Urs
- Last Active Sep 25th 2012

Created Lévy hierarchy.

- Discussion Type
- discussion topicfree module
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 24th 2012

added to

*free module*and to*submodule*a remark on the characterization of submodules of free modules.

- Discussion Type
- discussion topiclinear equation
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Sep 24th 2012

I finally started

*linear equation*. But am too tired now to really do it justice…

- Discussion Type
- discussion topichomotopy category of chain complexes
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 24th 2012

thought we’d need an entry

*homotopy category of chain complexes*

- Discussion Type
- discussion topicstratified space : strange typos { instead of -
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by TobyBartels
- Last Active Sep 24th 2012

In stratified space, many of the references had page numbers given as if 123 { 234, rather than 123 - 234. This is probably a paste from somewhere else, but I was wondering how it happened so as to avoid it myself. I changed it. (Might it be a strange font?)

- Discussion Type
- discussion topicquasi-isomorphism
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Sep 24th 2012

I have touched

*quasi-isomorphism*, expanded the Idea-section and polished the Definition-section, added References

- Discussion Type
- discussion topicC(n)-extendible cardinals and refining Vopenka's principle
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Sep 24th 2012

Recorded some facts from http://arxiv.org/abs/1101.2792 at supercompact cardinal, Vopenka’s principle, and a newly created page C(n)-extendible cardinal (with bonus stub for [[extendible cardinal]).

- Discussion Type
- discussion topicDeductions/derivations
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Sep 23rd 2012

Urs had a framework at deduction and I put in something very brief. Also disambiguation at derivation.

- Discussion Type
- discussion topicRussell's paradox
- Category Latest Changes
- Started by Mike Shulman
- Comments 10
- Last comment by Tim_Porter
- Last Active Sep 23rd 2012

Created Russell’s paradox.

- Discussion Type
- discussion topicenough projectives/injectives
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 23rd 2012

I have given the section

*Existence of enough injectives*at*injective object*a bit of structure. Then I started adding some similar basics to*Existence of enough projectives*at*projective object*.

- Discussion Type
- discussion topicBurali-Forti's paradox
- Category Latest Changes
- Started by Mike Shulman
- Comments 30
- Last comment by TobyBartels
- Last Active Sep 23rd 2012

Created Burali-Forti’s paradox.

- Discussion Type
- discussion topicsequent
- Category Latest Changes
- Started by Urs
- Comments 51
- Last comment by TobyBartels
- Last Active Sep 23rd 2012

For some text I need to explain the relation between

*sequents*in the syntax of dependent type theory and*morphisms*in their categorical semantics.I wanted to explain this table:

$\,$ types terms (∞,1)-topos theory $\;\;\;\;X \stackrel{\vdash \;\;\;\;E}{\to} \;\;\Type$ $\;\;\;\;X \stackrel{\vdash \;\;\;t}{\to} {}_X \;\;E$ homotopy type theory $x : X \vdash E(x) : Type$ $x : X \vdash t(x) : E(x)$ So I was looking for a place where to put it. This way I noticed that

*sequent*used to redirect to*sequent calculus*. I think this doesn’t do justice to the notion and so I havesplit off a new entry

*sequent*added a brief Idea-blurb

added my table and some explanation leading up to it

leaving the whole entry in genuinely stubby state. But no harm done, I think, if we compare to the previous state of affairs.

- Discussion Type
- discussion topicover-(oo,1)-topos
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 22nd 2012

splitt off an entry over-(infinity,1)-topos with material that had been scattered elsewhere and needed to be collected in order to allow referencing it

- Discussion Type
- discussion topicsyzygy
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Tim_Porter
- Last Active Sep 21st 2012

started

*syzygy*.

- Discussion Type
- discussion topicinconsistency
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by TobyBartels
- Last Active Sep 21st 2012

I have created stubs for

*inconsistency*and*contradiction*

- Discussion Type
- discussion topicuse of category: blah
- Category Latest Changes
- Started by Tim_Porter
- Comments 18
- Last comment by TobyBartels
- Last Active Sep 21st 2012

I have been adding various entries to various categories such as infinity groupoid was added to category:∞-groupoid, as it was not there! This is partially for my information as I have forgotten what entries there are on things of current interest to me, but it will explain why there seem to be a lot of entries changed by me but not in substance.

- Discussion Type
- discussion topicVojta's conjecture
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Sep 20th 2012

- Discussion Type
- discussion topiclooping combinator
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by Mike Shulman
- Last Active Sep 20th 2012

Created looping combinator.

- Discussion Type
- discussion topicinfinity-module
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Sep 20th 2012

I noticed that in

the

*∞-module*was kind of missing (we had module over an algebra over an (∞,1)-operad). So I created something stubby.

- Discussion Type
- discussion topictype of types
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 20th 2012

I have created an entry type of types. Wanted to collect some literature there, but ended up not finding too much…

- Discussion Type
- discussion topicterm
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 20th 2012

When making

*inhabitant*redirect to*term*a few minutes back I also found the entry*term*to be in an unfortunate state. I tried to improve it a bit by giving it more of an Idea section, and at least a vague indication of the formal definition.

- Discussion Type
- discussion topicsalamander lemma
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Sep 20th 2012

I am starting

*salamander lemma*

- Discussion Type
- discussion topicimplication
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 20th 2012

at

*implication*there is currently the statement$q \to r \vdash (p \to q) \to (q \to r)$,

That’s a typo, right?

- Discussion Type
- discussion topicreal coalgebra
- Category Latest Changes
- Started by Todd_Trimble
- Comments 10
- Last comment by Todd_Trimble
- Last Active Sep 19th 2012

I hope to be adding bits and pieces to an article real coalgebra, which I’ve started. (In some sense it might fit better on my web, but for some reason I’m placing it on the main nLab.)

- Discussion Type
- discussion topicextension of scalars
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 19th 2012

I ended up spending some time with expanding

*extension of scalars*. Towards the end I had more plans, but I’ll stop now, need to do something else.

- Discussion Type
- discussion topicindex of a subgroup
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 19th 2012

created

*index of a subgroup*

- Discussion Type
- discussion topicfour lemma
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 18th 2012

created

*four lemma*(should still state the dual version, will do so later)

- Discussion Type
- discussion topicequality and equivalence - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 18th 2012

and now I even ended up creating a new floating table of contents:

*equality and equivalence - contents*(all I wanted to originally was to create an elementary entry

*linear equation*…)

- Discussion Type
- discussion topicequation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 17th 2012

I really just wanted to start an entry

*linear equation*but I ended up putting some content into*equation*.

- Discussion Type
- discussion topicLascar group and first order theories
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Sep 17th 2012

I have added some links to preprint on the entry Lascar group. I do not understand the model theory, but its link with Galois theory may be of use to someone looking at model theory and type theory elsewhere on the Lab, so I hope it is useful.

- Discussion Type
- discussion topicinternal set
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by TobyBartels
- Last Active Sep 17th 2012

I see we have

*internal set*, while I was just about to make that term redirect to*Bishop set*.That would have read more systematically in the list at

*internal infinity-categories contents*.

- Discussion Type
- discussion topicformal logic
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 15th 2012

I keep feeling the need to point to an entry named

*formal logic*. None of the existing entries seems to quite deserve to be where this link should be redirecting to. So I created a page*formal logic*with just some pointers to pages that the reader*might*expect behind this term.Just so that I can use that link for the time being.

- Discussion Type
- discussion topicDrinfeld associators
- Category Latest Changes
- Started by adrienBrochier
- Comments 4
- Last comment by adrienBrochier
- Last Active Sep 15th 2012

- I created and filled a bit a page about Drinfeld associators.

- Discussion Type
- discussion topicHamiltonian form
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 15th 2012

have split off

*Hamiltonian form*from n-plectic geometry (because I needed to be able to point to it)

- Discussion Type
- discussion topicDrinfeld-Kohno Lie algebra
- Category Latest Changes
- Started by adrienBrochier
- Comments 3
- Last comment by adrienBrochier
- Last Active Sep 14th 2012

- Expanded a bit Drinfeld-Kohno Lie algebra

- Discussion Type
- discussion topicSimple functions
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Sep 14th 2012

I took simple function out of measure space, putting there abstract definitions up through the integral on $L^1$.

- Discussion Type
- discussion topicconnecting homomorphism
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 12th 2012

creatd connecting homomorphism with (just) the pedestrian description.

(Relation to snake lemma and more generally to fiber sequences not there yet…)

- Discussion Type
- discussion topicGrothendieck universe
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2012

added at

*Grothendieck universe*at References a pointer to the proof that these are sets of $\kappa$-small sets for inaccessible $\kappa$. (also at inaccessible cardinal)

- Discussion Type
- discussion topicuniverse - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2012

As I said in another thread, I would like to see the $n$Lab entries related to universes be somehow better, more organized, more comprehensive.

In order to get a handle on it I decided, as so often, to tabulate what we have and what we should have, so I am creating:

and will include it as a “floating table of contents” into the relevant entries

- Discussion Type
- discussion topicinductive reasoning
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by TobyBartels
- Last Active Sep 11th 2012

at

*inductive reasoning*it saysInduction here is not to be confused with

*mathematical induction*.We should point out that, however, there is a close relation:

one can see this still in the German tem for, “induction over the natural numbers” which is not

*Induktion*, but*vollständige Induktion*: meaning ”*complete*induction” !I guess the reasoning is clear, mathematical induction (at least that over the natural numbers)

*is*a special case of inductive reasoning, namely that where we can be sure that we are inducing from a*complete*set of instances of the general rule.Does anyone feel like touching the entry accordingly to clarify this?

- Discussion Type
- discussion topicbimonoidal category
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Mike Shulman
- Last Active Sep 11th 2012

stub for bimonoidal category

- Discussion Type
- discussion topicdirect sum
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2012

I have touched the formatting at

*direct sum*and then expanded a little:Added a paragraph to the Idea-section such that something familiar is mentioned right at the beginning;

Expanded on the example of direct sums in $Ab$ by drawing the cocone diagrams and explicitly mentioning the universal property.

Mentioned the relation to formal linear combinations.

Mentioned the examples of direct sums of modules.

- Discussion Type
- discussion topicMod
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Sep 11th 2012

created Mod

- Discussion Type
- discussion topicquotient module
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2012

created

*quotient module*

- Discussion Type
- discussion topicsubmodule
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2012

created

*submodule*

- Discussion Type
- discussion topicquotient group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2012

turns out plenty of entries were asking for

*quotient group*. I created something. But am running a bit out of steam for tonight.

- Discussion Type
- discussion topiccokernel
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 11th 2012

I have touched

*cokernel*, briefly adding some basics. More needs to be done here.

- Discussion Type
- discussion topicstructure
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Mike Shulman
- Last Active Sep 10th 2012

After discussion here I have changed the organization of the entry

*structure*and then expanded a bit by adding an Idea-section and a bit more here and there.(The previous organization of the entry instead made it look like

*structure in model theory*is a concept on par with that discussed at*stuff, structure, property*. But instead, the latter axiomatizes the general notion of “structure on something” as such, whereas the former is an*example*of a structure on something (namely an “$L$-structure on a set”). The new version aims to reflect this properly.)