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QFT on non-commutative spacetime, for the moment just to record a review paper
Created Dedekind completion. Probably not very satisfactory, but I lifted the main definition from Paul Taylor’s page on Dedekind cuts, so should be ok with a little tweaking.
needed matter to point somewhere
Since it appeared as a prominent grey link in integration of differential forms (and is a grey link in many other places), I wrote absolutely continuous measure.
as mentioned in another thread, I have created an entry minimal coupling
stub for divisible group
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.
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 , and some other spectra, but believed to be false in general.
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 via -image factorization of the name of ?
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…)
added to composition a new section with trivial remarks on composition in enriched category theory.
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.
Created Lévy hierarchy.
added to free module and to submodule a remark on the characterization of submodules of free modules.
thought we’d need an entry homotopy category of chain complexes
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?)
I have touched quasi-isomorphism, expanded the Idea-section and polished the Definition-section, added References
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]).
Urs had a framework at deduction and I put in something very brief. Also disambiguation at derivation.
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.
Created Burali-Forti’s paradox.
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 | ||
| homotopy type theory |
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 have
split 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.
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
started syzygy.
I have created stubs for inconsistency and contradiction
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.
Created looping combinator.
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.
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.
I am starting salamander lemma
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.)
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.
created index of a subgroup
created four lemma (should still state the dual version, will do so later)
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…)
I really just wanted to start an entry linear equation but I ended up putting some content into equation.
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.
have split off Hamiltonian form from n-plectic geometry (because I needed to be able to point to it)
I took simple function out of measure space, putting there abstract definitions up through the integral on .
creatd connecting homomorphism with (just) the pedestrian description.
(Relation to snake lemma and more generally to fiber sequences not there yet…)
As I said in another thread, I would like to see the 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
at inductive reasoning it says
Induction 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?
created submodule
turns out plenty of entries were asking for quotient group. I created something. But am running a bit out of steam for tonight.
I have touched cokernel, briefly adding some basics. More needs to be done here.
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:
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.
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. :-)
I finally gave the poor entry physics a bit of text.
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?
Expanded second-countable space and started first-countable space.
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.)
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.
Created κ-ary site.
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.