Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

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 homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limit 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 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 stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes

Show all

13141 to 13200 of 14796

  1. <
  2. 1
  3. ...
  4. 216
  5. 217
  6. 218
  7. 219
  8. 220
  9. 221
  10. 222
  11. 223
  12. ...
  13. 247
  14. >

    • started complex analytic space

      but I really have some basic questions on this topic, at the time of posting this I am really a layperson:

      is it right that every complex analytic space is locally isomorphic to a polydisk?

      So then they are all locally contractible as topological spaces. Are they also locally contractible as seen by étale homotopy? (So: do they admit covers by polydsisks such that if in the Cech-nerves of these covers all disks are sent to points, the resulting simplicial set is contractible?)

    • I have added some information on the work of Henry Whitehead which is related to this topic, and referred to work of Graham Ellis, and of Higgins and I, which is relevant.

      I expect I have not given the best code for all of this so someone may want to improve it in that respect.

      Graham, also writes in his paper:

      In view of the ease with which Whitehead's methods handle the
      classifications of Olum and Jajodia, it is surprising that the
      papers \cite{olum:1953} and \cite{jaj:1980} (both of which were
      written after the publication of \cite{whjhc:1949}) make
      respectively no use, and so little use, of \cite{whjhc:1949}.

      We note here that B. Schellenberg, who was a student of Olum, has
      rediscovered in \cite{sch:1973} the main classification theorems
      of \cite{whjhc:1949}. The paper \cite{sch:1973} relies heavily on
      earlier work of Olum.

    • I came to wonder about the words “empty context” in type theory, for what is really the context of the unit type. For there is also the context of the empty type.‘ That that might also seem to be called the “empty context”.

      I suppose nobody probably bothers to call the context of the empty type anything, because type theory over the empty type is the empty theory. :-)

      But still, it feel terminologogically unsatisfactory. Any suggestions?

      Would it not be better to speak of the unit context instead of the empty context for the context of the unit type?

      Also, I keep thinking that type theory in the context of the empty type is not entirely without use. For instance it appears in the type-theoretic version of what topos-theoretically is the base change maps over

      ∅→Type→* \emptyset \to Type \to *

      and that is the codomain fibration

      H /Type→H \mathbf{H}_{/Type} \to \mathbf{H}

      with its strutcure as a pointed map remembered, since the point is

      *≃H /∅. * \simeq \mathbf{H}_{/\emptyset} \,.

      I don’t know yet if this is super-relevant for anything, but it seems non-irrlelevant enough not to preclude it from being speakable.

    • 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

    • 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 BPBP, E(n)E(n) 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 Aut(X)\mathbf{Aut}(X) via ∞\infty-image factorization of the name of XX?

    • 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.

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

    • 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

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

    • 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→⊢EType\;\;\;\;X \stackrel{\vdash \;\;\;\;E}{\to} \;\;\Type X→⊢t XE\;\;\;\;X \stackrel{\vdash \;\;\;t}{\to} {}_X \;\;E
      homotopy type theory x:X⊢E(x):Typex : X \vdash E(x) : Type x:X⊢t(x):E(x)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 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

    • 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.

    • 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.

    • at implication there is currently the statement

      q→r⊢(p→q)→(q→r) q \to r \vdash (p \to q) \to (q \to r) ,

      That’s a typo, right?

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

    • 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.

    • 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 nnLab 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:

      universe - contents

      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?

    • turns out plenty of entries were asking for quotient group. I created something. But am running a bit out of steam for tonight.

13141 to 13200 of 14796

  1. <
  2. 1
  3. ...
  4. 216
  5. 217
  6. 218
  7. 219
  8. 220
  9. 221
  10. 222
  11. 223
  12. ...
  13. 247
  14. >
Top of Page