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).
    • Introduced the notion of derivation relative to a group homomorphism which can sometimes be a neat notion to have when discussing relative abelianisations.

      diff, v8, current

    • there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).

      I have added a remark on this in the (g2)(g-2)-entry here and also at quantum gravity here.

    • Starting something. Not done yet, but need to save.

      v1, current

    • Add more details and links to the references.

      diff, v4, current

    • added to groupoid a section on the description in terms of 2-coskeletal Kan complexes.

    • Adjusted the wording of the Idea-section for clarity and flow, and hyperlinked more of the technical terms.

      diff, v15, current

    • Added sidebar, TOC, links to references, citations. Fixed a broken link.

      Rongmin Lu

      diff, v4, current

    • Todd,

      when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

      Thanks!

    • started adding something (the example of the Hopf fibration and some references).

      What’s a canonical reference on the Whitehead products corresponding to the Hopf fibrations? Like what is an original reference and what is a textbook account?

      diff, v11, current

    • Created page, mainly to record my understanding of the issue involving strong normalization, or lack thereof, for explicit substitutions.

      v1, current

    • I made the former entry "fibered category" instead a redirect to Grothendieck fibration. It didn't contain any addition information and was just mixing up links. I also made category fibered in groupoids redirect to Grothendieck fibration

      I also edited the "Idea"-section at Grothendieck fibration slightly.

      That big query box there ought to be eventually removed, and the important information established in the discussion filled into a proper subsection in its own right.

    • added to Grothendieck construction a section Adjoints to the Grothendieck construction

      There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.

      There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.

    • I added more info on pseudo double categories and double bicategories to double category. I also simplified the picture of a square, which had been bristling with scary unnecessary detail. There's a slight blemish in the left vertical arrow, which I can't see how to fix.
    • I came across a reference to these, so started something.

      v1, current

    • I rescued combinatory logic from being a “my first slide” spam and gave it some content, mainly to record the fact (which I just learned) that under propositions as types, combinatory logic corresponds to a Hilbert system.

      I feel like there should be something semantic to say here too, like λ\lambda-calculus corresponding to a “closed, unital, cartesian multicategory” (a cartesian multicategory that is “closed and unital” as in the second example here) and combinatory logic corresponding to a closed category that is also “cartesian” in some sense. Has anyone defined such a sense?

      Relatedly, is there a notion of “linear combinatory logic” that would correspond to ordinary (symmetric) closed categories? My best guess is that instead of SS and KK you would have combinators with the following types:

      (BC)(AB)(AC) (B\to C) \to (A\to B) \to (A\to C) (A(BC))BAC (A \to (B\to C)) \to B \to A\to C

      coming from the two ways to eliminate a dependency in SS to make it linear (KK is irreducibly nonlinear). These are of course the ways that you express composition and symmetry in a closed category.

    • As i have obtained everything from MYSELF AS IM THE GLOBAL SOLO DADABASE ACROSS the world being taken away from me AND HES ON A MISSION AND I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with

      Anonymous

      v1, current

    • I updated a link on FGA explained to one of the chapters, to point to the arXiv version (the one on constructing Hilbert and Quot schemes). I also added a link to the conference page itself, which has links to scans of lecture notes, as the direct lecture notes links seem to be broken.

    • starting something – not done yet, but need to save

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • somebody asked me for the proof of the claim at canonical topology that for a Grothendieck topos H\mathbf{H} we have HSh can(H)\mathbf{H} \simeq Sh_{can}(\mathbf{H}).

      I have added to the entry pointers to the proof in Johnstone’s book, and to related discussion for \infty-toposes. Myself I don’t have more time right now, but maybe somebody feels inspired to write out some details in the nLab entry itself?

    • for completeness, with pointer to

      • Alexander Grothendieck et al., 16.5.15 in: Éléments de géométrie algébrique IV_4. Étude locale des schémas et des morphismes de schémas (Quatrième partie) Inst. Hautes Études Sci. Publ. Math. 32 (1967), 5–361. Ch.IV.§16–21 (numdam:PMIHES_1967__32__5_0)

      v1, current

    • a stub, for the moment just so as to give a home to

      • William Lawvere, Functional Remarks on the General Concept of Chaos , IMA reprint 87, 1984 (pdf)

      v1, current

    • Added some discussion (here) of chaotic groupoids on groups as models for their universal principal bundle.

      diff, v13, current

    • a bare list of entries on (n,r)(n,r)-toposes, for varying (n,r)(n,r), to be !include-ed under “Related concepts” in all relevant entries, for ease of synchronizing the cross-linking

      v1, current

    • added pointer (below a new Proposition-environment here) to where Paré states/proves the characterizations of L-finite limits (namely on his p. 740, specifically in his Prop. 7 – this also makes clear which typo the footnote is about).

      Similarly I added pointer (below a new Remark-environment here) to where Paré discusses the relation to K-finitness (namely the next page), together with attribution to Richard Wood.

      diff, v6, current