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- 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 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 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 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 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 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 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 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 topicNew SVGs for knot pages
- Category Latest Changes
- Started by Andrew Stacey
- Comments 21
- Last comment by Andrew Stacey
- Last Active Sep 10th 2012

Using the LaTeX macro package TikZ, I’ve redrawn most of the SVGs on the knots and links pages. I hope that I haven’t trodden on any toes in so doing! I may have missed a few diagrams as well.

I’ve shifted the actual SVGs to pages of their own. This makes it easier to edit the pages with them on - TikZ’s SVG export isn’t as compact as the inbuilt SVG editor - and easier to include on other pages. For example, I can imagine that the trefoil knot is going to appear again and again!

(Incidentally, are the two trefoils distinct? If so, which have I drawn at trefoil knot - SVG).

I’ve named the pages with

`- SVG`

in their name, though for the moment I’ve also put in redirects to the name without the SVG. When actually including the diagram, one should always use the*canonical*name (ie*with*the`- SVG`

) since it may be that we actually write a page about the trefoil knot one day. But I thought that for the moment, a nice aspect of hyperlinks is that if we mention the trefoil knot in a page then we can put in a link to an actual picture.Diagrams done so far:

- trefoil knot - SVG
- trefoil knot (2 bridge) - SVG
- Hopf link - SVG
- Whitehead link - SVG
- Borromean link - SVG (also redirects from Borromean rings)
- Reidemeister move 1 - SVG (it’s amazing how many ways it is possible to misspell Reidemeister)
- Reidemeister move 2 - SVG
- Reidemeister move 3 - SVG
- figure 8 knot - SVG

Pages with includes include: link, Reidemeister move, colorability, bridge number.

What would be fantastic here is if the “source” link took one to the actual LaTeX/TikZ source! I do intend to put that up on the nLab, but I need to clean it up a little as it depends on some customised style files that have a lot of crud in them.

- Discussion Type
- discussion topicAlexander, Dehn, et al
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Sep 10th 2012

I have been attacking some of the grey links in knot theory and the related pages. If someone has the time (and the patience) adding a few more links would be a good thing. I have added Crowell, Fox, Dehn, Alexander, Louis Kauffman, plus some non-people pages such as Alexander polynomial. That needs some diagrams if it is to do what it ’should’ and my svg skills are too slight to attempt that today. :-)

- Discussion Type
- discussion topicphysics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 8th 2012

I finally gave the poor entry

*physics*a bit of text.

- Discussion Type
- discussion topiclogic and inductive inference
- Category Latest Changes
- Started by David_Corfield
- Comments 32
- Last comment by TobyBartels
- Last Active Sep 8th 2012

Made some changes at logic and started inductive inference and George Polya.

There are still things to change at logic

As a discipline, logic is the study of methods of reasoning. While in the past (and often today in philosophical circles), this discipline was prescriptive (describing how one should reason), it is increasingly (and usually in mathematical circles) descriptive (describing how one does reason).

Could whoever wrote it explain what they meant? Seems odd to me.

Also I don’t think that category-theoretic logic should be there. Should it not appear in mathematical logic, or be a new page?

- Discussion Type
- discussion topic*-countable spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Sep 8th 2012

Expanded second-countable space and started first-countable space.

- Discussion Type
- discussion topicJohn Power
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Sep 7th 2012

I fixed a strange link at John Power.

- Discussion Type
- discussion topicfoundational axiom
- Category Latest Changes
- Started by Urs
- Comments 56
- Last comment by Mike Shulman
- Last Active Sep 6th 2012

To Toby, mainly, of course also to anyone interested:

We have a page-“category”

*foundational axiom*, but we have no entry of that name. We should start one!*foundational axiom*.(We do have

*axiom of foundation*. A bit of a different thing.)

- Discussion Type
- discussion topicsecond order arithmetic
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by TobyBartels
- Last Active Sep 6th 2012

I’ve been editing second order arithmetic (I usually write “second-order arithmetic”, with a hyphen). I would appreciate someone taking a look and making corrections if necessary. There are probably some hyperlinks which could be added.

- Discussion Type
- discussion topicκ-ary site
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Sep 6th 2012

Created κ-ary site.

- Discussion Type
- discussion topick-ary exact category
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by Urs
- Last Active Sep 5th 2012

I renamed familial regularity and exactness to k-ary exact category (with redirects from k-ary regular category), and updated some of the statements to match my exact completions paper a bit better.

I’m planning to create k-ary site as well, and add a statement of the main theorem of the paper somewhere on the nLab. But I’m undecided as to where that statement should go and how it should interact with the existing pages regular and exact completions and pretopos completion. Opinions are welcome.

- Discussion Type
- discussion topicChan-Paton bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 5th 2012

expanded at

*Chan-Paton bundle*the Idea-section and added two pointers to lecture notes. Also expanded at*Freed-Witten anomaly*a little.

- Discussion Type
- discussion topictype theory - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2012

I ended up polishing

*type theory - contents*(which is included as a floating table of contents in the relevant entries):expanded and re-arranged the list under “syntax”, created stubs for the missing items

*definition*and*program*expanded the (logic/type theory)-table to a (logic/category theory/type theory)-table and subsumed some of the items into it that were floating around elsewhere.

- Discussion Type
- discussion topicaxiom of choice in type theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Sep 4th 2012

at

*axiom of choice*into the section*In dependent type theory*I have moved the explicit statement taken from the entry of dependent type theory (see there for what I am talking about in the following).One technical question: do we need the

`: true`

at the very end of the formal statement of the theorem?

One conceptual question: I feel inclined to add the following Remark to that, on how to think about the fact that the axiom of choice is always true in this sense in type theory. But please let me know what you think:

Heuristically, the reason that the axiom of choice is always true when formulated internally this way in dependent type theory is due to the fact that its

*assumption*thereby is stated in*constructive mathematics*:Stated in informal but internal logic, the axiom of choice says:

*If $B \to A$ is a map all whose fibers are inhabited, then there is a section.*But now if we interpret the assumption clause

*a map all whose fibers are inhabited*constructively, we have to provide a

*constructive proof*that indeed the fibers are inhabited. But such a constructive proof*is*a choice of section.So constructively and internally the axiom is reduced to “If there is a section then there is a section.” And so indeed this is always true.

Would you agree that this captures the state of affairs?

- Discussion Type
- discussion topicpseudocircle
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Sep 4th 2012

stub for

*pseudocircle*(a finite topological space)

- Discussion Type
- discussion topicfundamental group
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 8
- Last comment by Tim_Porter
- Last Active Sep 3rd 2012

- I added a sentence to fundamental group which contains a link to an example for a fundamental group of an affine scheme.

- Discussion Type
- discussion topictotal complex
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 3rd 2012

split off

*total complex*from*double complex*. Let the Definition-section stubby, as it was, but added a brief remark on exactness and on relation to total simplicial sets, under Dold-Kan and Eilenberg-Zilber. More to be done.

- Discussion Type
- discussion topicinterval object in chain complexes
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tim_Porter
- Last Active Sep 3rd 2012

- Discussion Type
- discussion topicStructural rules.
- Category Latest Changes
- Started by TobyBartels
- Comments 9
- Last comment by Mike Shulman
- Last Active Sep 3rd 2012

Stubs for structural rule, weakening rule, contraction rule, and exchange rule.

- Discussion Type
- discussion topicdichotomy
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by Urs
- Last Active Sep 2nd 2012

Speaking of philosophy, I added a little to dichotomy between nice objects and nice categories.

- Discussion Type
- discussion topicAn Introduction to Homological Algebra
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Sep 2nd 2012