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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nforum nlab noncommutative noncommutative-geometry number-theory object 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 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).

nLab > Latest Changes

Show all

181 to 240 of 10158

  1. <
  2. 1
  3. 2
  4. 3
  5. 4
  6. 5
  7. 6
  8. 7
  9. 8
  10. ...
  11. 170
  12. >

    • this is a bare little section, to be !include-ed as a Properties-subsection at slice category and adjoint (∞,1)-functor (where two copies of this same section used to be all along) and also at slice (∞,1)-category and adjoint functor (where, for completeness, the same should be recorded, too, but wasn’t until now)

      It would also be good to expand a little here, for instance by adding a pointer to a 1-category textbook account (this is probably in Borceux, but I haven’t checked yet), or, of course, by adding some indication of the proof.

      v1, current

    • am recording an actual proof that

      ℒ(W¯𝒢)≃𝒢 ad⫽𝒢 \mathcal{L} \big( \overline{W}\mathcal{G} \big) \;\; \simeq \;\; \mathcal{G}_{ad} \sslash \mathcal{G}

      I expected that a proof for this folklore theorem would be citeable from the literature, but maybe not quite. This MO reply points to Lemma 9.1 in arXiv:0811.0771, which has the idea (in topological spaces), but doesn’t explicitly verify all ingredients. I have tried to make it fully explicit (in simplicial sets).

      v1, current

    • am starting some minimum here. Have been trying to read up on this topic. This will likely become huge towards beginning of next year

      v1, current

    • I added a reference to a paper of mine

      Amnon Yekutieli

      diff, v48, current

    • Page created, but author did not leave any comments.

      v1, current

    • added earlier publication items:

      • Sören Illman, Equivariant singular homology and cohomology for actions of compact lie groups (doi:10.1007/BFb0070055) In: H. T. Ku, L. N. Mann, J. L. Sicks, J. C. Su (eds.), Proceedings of the Second Conference on Compact Transformation Groups Lecture Notes in Mathematics, vol 298. Springer 1972 (doi:10.1007/BFb0070029)

      • Sören Illman, Equivariant algebraic topology, Annales de l’Institut Fourier, Tome 23 (1973) no. 2, pp. 87-91 (doi:10.5802/aif.458)

      and also more cross-links under “Related entries”

      diff, v5, current

    • Someone anonymous has raised the question of subdivision at cellular approximation theorem. I do not have a source here in which I can check this. Can anyone else check up?

    • fixed the pointers to alleged proofs of the equivariant Whitehead theorem.

      What is a canonical citation for this statement, for the unstable case, citable as an actual proof? Is it due to Bredon? Is it in his book?

      diff, v3, current

    • In this entry I mean to write out a full proof for the transgression formula for (discrete) group cocycles, using just basic homotopy theory and the Eilenberg-Zilber theorem.

      Currently there is an Idea-section and the raw ingredients of the proof. Still need to write connecting text. But have to interrupt for the moment.

      v1, current

    • added to simplicial set in the Definition section a slightly more explicit version of the definition.

      (I see now this kind of thing is repeated further below in the entry. But it should be right there as a formal definition, I think.)

    • I added to cylinder object a pointer to a reference that goes through the trouble of spelling out the precise proof that for XX a CW-complex, then the standard cyclinder X×IX \times I is again a cell complex (and the inclusion X⊔X→X×IX \sqcup X \to X\times I a relative cell complex).

      What would be a text that features a graphics which illustrates the simple idea of the proof, visualizing the induction step where we have the cylinder over X nX_n, then the cells of X n+1X_{n+1} glued in at top and bottom, then the further (n+1)(n+1)-cells glued into all the resulting hollow cylinders? (I’d like to grab such graphics to put it in the entry, too lazy to do it myself. )

    • Since we had bits and pieces of this scattered around over several entries, I am giving this its own little entry, so as to have the statement and all relevant references collected in one place, for ease of updating/synchronizing and hyperlinking.

      v1, current

    • giving this its own little entry, for ease of hyperlinking

      v1, current

    • The term simplicial abelian group used to redirect to simplicial group. I am giving it its own little entry now, for better hyperlinking.

      v1, current

    • division rigs, the rig version of division rings

      Anonymous

      v1, current

    • Just a stub for the moment to try to introduce the notion of differential category due to Blute, Cockett and Seely.

      v1, current

    • Started writing down the definition.

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • Added some remark on the order of a semiring. Actually, does anybody know if any semiring embedds into a semifield?

      diff, v5, current

    • Created this entry with mention of lattice structure and a fundamental theorem of algebra for semifields.

      v1, current

    • added redirect plus some ‘selected publications’.

      diff, v2, current

    • added redirects for abbreviations of his name, plus some publications. Also added a (for the moment Grey link) to differential category, which hopefully I will be able to add a sutb for later.

      diff, v4, current

    • Found this abandoned stub entry from 2010. Have removed the line

      Zoran: This is just a reminder for me to work on this entry in few days (to do list)

      and instead added some minimum structure, including formatting, a line in the Idea-section (but not doing it justice) and some more references.

      diff, v2, current

    • some minimum, for the moment just for the convenience that the link works

      (in creating this entry I noticed that we have an ancient stub entry mapping complex that deserves some attention)

      v1, current

    • Fixed the comments in the reference list at model structure on dg-algebras: Gelfand-Manin just discuss the commutative case. The noncommutative case seems to be due to the Jardine reference. Or does anyone know an earlier one?

    • The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.

      diff, v19, current

    • I have added to monoidal model category statement and proof (here) of the basic statement:

      Let (𝒞,⊗)(\mathcal{C}, \otimes) be a monoidal model category. Then 1) the left derived functor of the tensor product exsists and makes the homotopy category into a monoidal category (Ho(𝒞),⊗ L,γ(I))(Ho(\mathcal{C}), \otimes^L, \gamma(I)). If in in addition (𝒞,⊗)(\mathcal{C}, \otimes) satisfies the monoid axiom, then 2) the localization functor γ:𝒞→Ho(𝒞)\gamma\colon \mathcal{C}\to Ho(\mathcal{C}) carries the structure of a lax monoidal functor

      γ:(𝒞,⊗,I)⟶(Ho(𝒞),⊗ L,γ(I)). \gamma \;\colon\; (\mathcal{C}, \otimes, I) \longrightarrow (Ho(\mathcal{C}), \otimes^L , \gamma(I)) \,.

      The first part is immediate and is what all authors mention. But this is useful in practice typically only with the second part.

    • I started an idea section at transgression, but it could probably use some going over by an expert. I hope I didn’t mess things up too badly. I was reading Urs’ note on “integration without integration” on the train ride home and fooled myself into thinking I understood something.

      By the way, this reminded me of a discussion we had a while back

      Integrals: Loops space vs target space

181 to 240 of 10158

  1. <
  2. 1
  3. 2
  4. 3
  5. 4
  6. 5
  7. 6
  8. 7
  9. 8
  10. ...
  11. 170
  12. >
Top of Page