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    • I have added to alternative algebra the characterization in terms of skew-symmetry of the associator.

    • I did a little editing over at empty set; the query-box discussion of 0 00^0 looked like it could be summarized with dispatch and relegated to a remark. Revert back or re-edit if you don’t like it.

    • I noticed that the entry disjoint union had no pointer to or from either of dependent sum, dependent sum type.

      I have added the bare pointers now (no energy for more now). But this means some basic examples are missing in these entries.

    • I was un-graying some links at epsilontic analysis. Among the titles of non-existing entries that are still being requested is

      • “classical analysis”

      • “topological property”.

      Is it likely/desireable that we will have entries with these titles? Maybe we should change these links to point to “analysis” and to “topology” instead?

    • I started an entry for Rijke’s join of maps. How do you place the *\ast lower?

    • I have added both to proof and to experiment pointer to

      with the quote (from p. 2):

      we claim that the role of rigorous proof in mathematics is functionally analogous to the role of experiment in the natural sciences

    • I added a remark about the contravariant Yoneda embedding c↦C(c,−)c \mapsto C(c,-) to the page on the Yoneda embedding.

      It’s pretty elementary, but I think worth mentioning for those new to category theory that this is just the Yoneda embedding of the opposite category Y:C op→[(C op) op,Sets]=[C,Sets]Y: C^{op} \to [(C^{op})^{op}, Sets]=[C, Sets].

    • I move null set to null subset and added more about how these are defined in unusual contexts.

    • I added the theorem that complete norms on a real vector space are unique (up to topological equivalence) at norm#dreamUnique. (This is false in classical mathematics, of course, but it’s true in dream mathematics.) Also true for F-norms.

    • expanded endomorphism operad

      (it’s still a bit rough, but I am a bit rushed and have no time to polish)

    • I added to uniformly regular space a definition of “uniform apartness space” and a proof that under uniform regularity, these coincide with ordinary uniform spaces. I think this is interesting because it seems to be one of the purposes of uniform regularity (and local decomposability).

    • I rescued an empty page and wrote F-norm.

    • This theorem, with a constructive proof, is now at convergence space. (The usual proof in undergraduate metric-space theory uses both excluded middle and countable choice1, so I wrote this mostly to verify that it is actually perfectly constructive in the general setting.)

      1. ETA: And the straightforward generalization to nonsequential spaces would use choice of arbitrarily high cardinality. ↩

    • Back in 2015, Bas Spitters wrote filter space. These are even more general than convergence spaces! (In a filter space, even if two filters both converge to the same point, their intersection might not.) I've put in the definition from the cited paper by Martin Hyland.

    • Since I wondered what they were, I started an entry Gorenstein ring spectrum, which then needed Gorenstein ring. Not sure I’m much the wiser as to their importance. There should be a lot to say about related duality.

    • I realized that we had a stub entry “configuration space” with the physics concept, and a stub entry “Fadell’s configuration space” with the maths concept, and no interrelation between them, also without any examples. So I created a disambiguation page

      and then

      but I also left

      separate for the moment, thinking that in principle the term in matematics may be understood more generally, too. But maybe something should be merged here.

      I added the example of the unordered configuration space of ℝ ∞\mathbb{R}^\infty as a model for the classifying space for the symmetric group to the relevant entries. But otherwise they do remain stubby, alas.

    • In the nLab article on the universal enveloping algebra, the section describing the Hopf algebra structure originally stated that “the coproduct Δ:UL→U(L∐L)≅UL⊗UL\Delta: U L \to U(L \coprod L)\cong U L\otimes UL is induced by the diagonal map L→L∐LL \to L \coprod L.”

      I assume that this is a mistake, and I have since changed the coproduct ∐\coprod to a product ×\times. However, I don’t know a great deal about Hopf algebras, so please correct me if I’ve made a mistake here.

    • In line with the “pages named after theorems” philosophy, I’ve created toposes are extensive, including in particular the (somewhat hard to track down) constructive proof that a cocomplete elementary topos is infinitary extensive.

    • I finally gave spectral super-scheme an entry, briefly stating the idea.

      This goes back to the observation highlighted in Rezk 09, section 2. There is some further support for the idea that a good definition of supergeometry in the spectrally derived/E ∞E_\infty context is nothing but E ∞E_\infty-geometry over even periodic ring spectra. I might add some of them later.

      Thanks to Charles Rezk for discussion (already a while back).

    • I added some results and references at Calkin algebra after I noticed that Zoran had added some comments about set-theoretic axioms leading to different properties. In particular the outer automorphism algebra of the Calkin algebra is trivial or not, depending on whether one has CH, or something that violates CH, Todocevic’s Axiom.

    • Created a page for DLO, the (first-order) theory of (ℚ,<)(\mathbb{Q},&lt;). Made some notes about model-theoretic properties, Cantor’s theorem that all countable models of the theory are isomorphic, and also remarked (based on an exercise from Mac Lane and Moerdijk) that the subobject classifier for the topos Set (ℚ,<)\mathbf{Set}^{(\mathbb{Q},&lt;)} can be naturally identified with the Dedekind cuts on ℚ\mathbb{Q}.

    • Created Fraïssé limit.

      (I was pleasantly surprised to see @David_Corfield had posted about the these things a while ago for the n-Category Cafe.)

      Mentioned a neat result of Olivia Caramello’s that omega-categorical structures presentable as Fraisse limits are determined by their automorphism groups GG with the topology of pointwise convergence in a very nice way: their classifying toposes are precisely the toposes of continuous GG-sets.

      To fill in a grey link, I also created an entry for the countable random graph.

    • created model structure on dg-comodules, just so as to record a pointer to Positelski 11, theorem 8.2.

      Regarding the dg-comodules which are injective as graded comodules over the underlying graded cocommutative co-algebra: Suppose the latter is co-free and the ground ring is a field. Is it then true that all injective comodules over it are cofree? Because this would seem to be a dual version of the Quillen-Suslin theorem?

    • I changed ‘SEAR is a dependent type theory’ at SEAR to ‘SEAR is a dependently typed theory’. A type theory is a general theory of types, including lots of type formation rules; SEAR is a theory of sets written in a dependently typed first-order logic with very few type formation rules.

      But I still linked to dependent type theory, since we don't seem to have good material on using type systems with first-order logic.

    • created a stub entry for comodule spectrum, for the moment just so as to briefly record the result by Hess-Shipley 14 that comodule spectra over suspension spectra of connected spaces XX are equivalently parameterized spectra over XX. Added that reference also to A-theory. Needs to be expanded further.

      (Thanks to Charles Rezk for the pointer.)

    • originating from another thread (here):

      jesse kindly created ultraroot. I have added some more hyperlinks to some more of the keywords.

    • for the purposes of having direct links to it, I gave a side-remark at stable Dold-Kan correspondence its own page: rational stable homotopy theory, recording the equivalence

      (Hℚ)ModSpectra≃Ch •(ℚ) (H \mathbb{Q}) ModSpectra \;\simeq\; Ch_\bullet(\mathbb{Q})

      I also added the claim that under this identification and that of classical rational homotopy theory then the derived version of the free-forgetful adjunction

      (dgcAlg ℚ ≥2) /ℚ[0]⊥⟶U∘ker(ε (−))⟵Sym∘cnCh •(ℚ) (dgcAlg^{\geq 2}_{\mathbb{Q}})_{/\mathbb{Q}[0]} \underoverset {\underset{U \circ ker(\epsilon_{(-)})}{\longrightarrow}} {\overset{Sym \circ cn}{\longleftarrow}} {\bot} Ch^{\bullet}(\mathbb{Q})

      models the stabilization adjunction (Σ ∞⊣Ω ∞)(\Sigma^\infty \dashv \Omega^\infty). But I haven’t type the proof into the entry yet.

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