Not signed in (Sign In)

Start a new discussion

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 beauty bundle bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched etcs fibration 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 lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure measure-theory modal modal-logic model model-category-theory 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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).
    • a stub entry, for the moment just to record some references

      v1, current

    • I understood that the old terminology was ’projective system’, and ’projective limit’ refereed to the limit of a projective system. Can anyone confirm that? if I am right the present entry is slightly incorrect, but this needs checking first before changing it.

    • I edited The Joy of Cats to link to metacategory and to disambiguate quasicategory, as twice now someone on MO has used the term ’quasicategory’ to talk about (very) large categories. This way, if people find the book using the nLab page they are forewarned.

      I also edited quasicategory to move the terminological warning up to the idea section where it is immediately visible, rather than in the second section, below the definition.

    • tried to improve the entry coproduct a little

    • I have added to coequalizer basic statements about its relation to pushouts.

      In the course of this I brought the whole entry into better shape.

    • added to equalizer statement and proof that a category has equalizers if it has pullbcks and products

    • Added material on diagonal maps and the product functor, mentioning for instance the fact that the product functor is right adjoint to a diagonal functor.

      diff, v22, current

    • added a Properties-section to pullback

    • I wrote out a proof that geometric realization of simplicial sets valued in compactly generated Hausdorff spaces is left exact, using essentially the observation that simplicial sets are the classifying topos for intervals, combined with various soft topological arguments. I left a hole to be plugged, that geometric realizations are CW complexes. I also added a touch to filtered limit, and removed a query of mine from triangulation.

      I wanted a “pretty proof” for this result on geometric realization, centered on the basic topos observation (due to Joyal). I was hoping Johnstone did this himself in his paper on “a topological topos”, but I couldn’t quite put it together on the basis of what he wrote, so my proof is sort of “homemade”. I wouldn’t be surprised if it could be made prettier still. [Of course, “pretty” is in the eye of the beholder; mainly I want conceptual arguments which avoid fiddling around with the combinatorics of shuffle products (which is what I’m guessing Gabriel and Zisman did), decomposing products of simplices into simplices.]

    • The entry Clifford algebra used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:

      Just the bare statements so far.

    • I have further expanded the Idea-section and the list of commented references at perturbative quantum field theory.

      (Not proof-read yet, need to run to catch a train.)

    • brief category:people-entry for hyperlinking references

      v1, current

    • am giving this its own page, for ease of cross-linking and referencing

      v1, current

    • am giving this its own little entry, for ease of reference

      v1, current

    • Changed ≤ to \lneq the subscript of the definition of elementary symmetric polynomial to match the wikipedia page. (< produced a latex error for some reason)

      Shane

      diff, v2, current

    • created a simple entry ring object, just for completeness

    • mathematical physics with a slight distinction from physical mathematics which points to the same entry. The relation to theoretical physics has been discussed, but I am not sure yet if we should have theoretical physics as a separate entry so I do not put is as another redirect.

    • This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>created <a href="http://ncatlab.org/nlab/show/nonabelian+group+cohomology">nonabelian group cohomology</a></p> <p>the secret title of this entry is "Schreier theory done right". (where "right" is right from the <a href="http://ncatlab.org/nlab/show/nPOV">nPOV</a>)</p> <p>this is the first part of the answer to</p> <blockquote> What is going on at <a href="http://ncatlab.org/nlab/show/nonabelian+Lie+algebra+cohomology">nonabelian Lie algebra cohomology</a>? </blockquote> <p>The second part of the answer is the statement:</p> <blockquote> The same. </blockquote> <p>;-)</p> <p>I'll expand on that eventually.</p> </div>
    • I added a reference to a paper of mine

      Amnon Yekutieli

      diff, v48, current

    • am giving this its own category:reference-entry, for better hyperlinking

      Have done the same for Groupprops

      v1, current

    • am giving this a category:reference-entry, too, for better hyperlinking

      Will do the same for GroupNames

      v1, current

    • a bare list of references, to be !include-ed into the References-list of relevant entries

      v1, current

    • created Einstein manifold

      (for the moment only to record the example of weak G 2G_2-manifolds…)

    • Added pointers concerning the suggestion that the observed Higgs mass is related to asymptotic safety.

      diff, v7, current

    • changing the page title (which used to be “Henry Whitehead”) for better identification

      diff, v13, current

    • I requested some more details at strict 2-category. It would be nice to have something describing how objects are categories, morphisms are ??? satisfying ???, 2-morphisms are ??? satisfying ???.

      I'm sure all the details could be unwrapped from the simple statement "a strict 2-category is a Cat-category", but then I need to learn what an enriched category is first and then I need to see how that works in the case of Cat-enriched category. Soon, I feel overwhelmed. A strict 2-category is probably not THAT hard to understand explicitly.

    • Correct the characterization of nerves of groupoids.

      diff, v54, current

    • Finally splitting this off from lattice QCD in order to record some references. Gave it a rough Idea-section, but this remains a stub.

      v1, current