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    • Created theorem-page to record the result and references.

      v1, current

    • Change text from ’m’ (since 2015!) to a real article.

      diff, v2, current

    • Added a section about the preservation of five classes of maps.

      diff, v11, current

    • A message to Mike:

      Hi Mike,

      I hear that in Swansea you ended by talking about things related to elementary ∞\infty-toposes. I didn’t get a chance to see anyone’s notes yets. Do you have electronic notes to share?

    • added pointer to

      • J. Montesinos, A representation of closed orientable 3-manifolds as 3-fold branched coverings of S 3S^3, Bull. Amer. Math. Soc. 80 (1974), 845-846 (Euclid:1183535815)

      here and also at 3-manifold and 3-sphere

      diff, v11, current

    • stub, for the moment just so as to make links work

      v1, current

    • Is the equivariant suspension spectrum functor still strong monoidal, homotopically?

      diff, v10, current

    • created brief entries Wirthmüller context and Grothendieck context, following Peter May’s terminology for the two special cases where four of the Grothendieck six operations specialize to an adjoint triple.

      The main thing I’d like to record is lists of classes of examples that realize either of these contexts. But haven’t gotten around to that yet.

    • Created new page for Brownian motion.

      Anonymous

      v1, current

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

      v1, current

    • Some minimal content, and a couple of examples.

      v1, current

    • Corrected an arithmetic error in the last section.

      diff, v14, current

    • a stub, for the moment just so as to make links work

      v1, current

    • just for completeness. Redirecting “positive definite matrix” and various variants of that.

      v1, current

    • Added something to fill a link. Please check the definition that I have given; it is the one that is most natural to me, but not the most standard! Feel free to add details of equivalent definitions.

      The commutative diagram will not render yet, I am working on that now; should be done shortly. [Edit: done now!]

      v1, current

    • Created page, recording the definition and its relation to awfs.

      v1, current

    • Creating this for testing the nForum announcer. I plan to fill it in with actual content soon.

      v1, current

    • Tried to discuss this notion in a way which has some flexibility and generality, but which also is concrete.

      v1, current

    • A beginning to satisfy some links.

      v1, current

    • a stub, for the moment just so as to make links work

      v1, current

    • am clearing this page, since I just noticed that it duplicates the entry Robion Kirby. I suppose the latter should be the entry with “Rob Kirby” a redirect(?)

      diff, v2, current

    • Created page, with definition.

      Berger-Mellies-Weber claim that the nerve theorem for monads with arities constructs Eilenberg-Moore and Kleisli objects in the 2-category of categories with arities, but as far as I can see their proof as written only shows that the Eilenberg-Moore adjunction lives in this 2-category, not that it retains its universal property there. Is there a quick way to see that it does? If this is true, then I think it gives an even more “natural” explanation of the nerve construction, along the lines of Tom’s original blog post.

      v1, current

    • added pointer to

      • R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter, On the Zeros of the Riemann Zeta Function in the Critical Strip. II, Mathematics of Computation Mathematics of Computation Vol. 39, No. 160 (Oct., 1982), pp. 681-688 (doi:10.2307/2007345 )

      for computer-checks of the Riemann hypothesis. (there are probably more recent such?)

      diff, v8, current

    • I gave sheaf with transfer an Idea-section

      (the entry used to me named “Nisnevich sheaves with transfer”. I have renamed it to singular to stay with our convention and removed the “Nisnevich” from the title, as the concept of transfer as such is really not specific to the Nisnevich topology).

      The idea section now is the following. (Experts please complain, and I will try to fine tune further):

      Given some category (site) SS of test spaces, suppose one fixes some category Corr p(S)Corr_p(S) of correspondences in SS equipped with certain cohomological data on their correspondence space. Then a sheaf with transfer on SS is a contravariant functor on Corr p(S)Corr_p(S) such that the restriction along the canonical embedding S→Corr p(S)S \to Corr_p(S) makes the resulting presheaf a sheaf.

      Traditionally this is considered for SS the Nisnevich site and Corr p(S)Corr_p(S) constructed from correspondences equipped with algebraic cycles as discussed at pure motive, (e.g. Voevodsky, 2.1 and def. 3.1.1).

      The idea is that, looking at it the other way around, the extension of a sheaf to a sheaf with transfer defines a kind of Umkehr map/fiber integration by which the sheaf is not only pulled back along maps, but also pushed forward, hence “transferred” (this concept of course makes sense rather generally in cohomology, see e.g. Piacenza 84, 1.1).

      The derived categories those abelian sheaves with transfers for the Nisnevich site with are A1-homotopy invariant provides a model for motives known as Voevodsky motives or similar (Voevodsky, p. 20).

    • Definition of extensional PiPi-type structure taken from Natural models of homotopy type theory

      Should we develop how to get application, β\beta and η\eta here or should we leave it to the interpretation ?

      v1, current

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

      v1, current

    • I hope I have fixed a link! (edit: It worked!)

      diff, v2, current

    • I added a note to the article on the subobject classifier: “In type theory, the type corresponding to the subobject classifier is typically called Prop.”

    • After Urs’ post at the café about “Tricategory of conformal nets” at Oberwolfach I took a look at the paper Conformal nets and local field theory and noted that I would have to ask some trivial and boring questions about nomenclature before I could even try to get to the content.

      One example is about “Haag duality”: It seems to me that we need a generalization of net index sets on the nLab that includes the bounded open sets used for the Haag-Kastler vacuum representation and the index sets used in the mentioned paper. One of the concept needed would be “causal index set”:

      A relation ⊥\perp on an index set (poset) II is called a causal disjointness relation (and a,b∈Ia, b \in I are called causally disjoint if a⊥ba \perp b) if the following properties are satisfied:

      (i) ⊥\perp is symmetric

      (ii) a⊥ba \perp b and c<bc \lt b implies a⊥ca \perp c

      (iii) if M⊂IM \subset I is bounded from above, then a⊥ba \perp b for all a∈Ma \in M implies supM⊥bsup M \perp b.

      (iv) for every a∈Ia \in I there is a b∈Ib \in I with a⊥ba \perp b

      A poset with such a relation is called a causal index set.

      Well, that’s not completly true, because in the literature that I know there is the additionally assumtion that II contains an infinite unbounded sequence and hence is not finite (that whould be a poset that is ? what? unbounded?), that is not a condition imposed on posets on the nLab.

      After this definition one can go on and define “causal complement”, the “causality condition” for a net and then several notions of duality with respect to causal complements etc. all without reference to Minkowski space or any Lorentzian manifolds.

      Should I create a page causal index set or is there something similar on the nLab already that I overlooked?

    • I started writing a bit more about FOLDS, and while I was at it I clarified the relationship between FOLDS' "simple categories]] and direct categories.

    • Attempt at making a page about defunctionalization. My first new page on nlab, I hope there are no faux pas’s. I noticed the resemblance to the adjoint functor theorem a while back, and several people seemed to find it interesting, so I thought I’d make a page.

      v1, current

    • Create page, add some initial references. Referenced from the ’category theory’ page.

      v1, current

    • Created stub for Spin group. Made a mess of explaining why it is so named.

      -David Roberts

    • a stub, am trying to bring into place some infrastructure for discussion of the finite subgroups of O(5)O(5)

      v1, current

    • starting a stub, for the moment just collecting references.

      Which finite subgroup of SO(4)SO(4) corresponds to the 120-cell?

      v1, current

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