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    • Created a stub to record a new article and to satisfy a link.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • some minimum prose on the Kitaev toric code, for the moment mostly just to make the link work and record some references

      v1, current

    • starting page on null types in dependent type theory

      Anonymouse

      v1, current

    • I just noticed and noted that Gabriella Böhm wrote a book, on generalizations in Hopf world,

      • Hopf algebras and their generalizations from a category theoretical point of view, Lec. Notes Math. 2226, Springer 2018

      diff, v9, current

    • Created a stub for cofunctor? with some references.

      v1, current

    • I created hypermonoid, polishing the comments I made in the hypermonoid thread into an article. The last subsection of the article mentions a general technique for constructing hypermonoids which ought to immediately suggest further examples to a quantum group specialist like Zoran, but I am not such a specialist. I also inserted some shameless self-promotion under References.

    • Removed the sentence

      “If XX has decidable equality, then the negation of equality is a (in fact the unique) tight apartness on XX, and any function from XX to any set YY (with any tight apartness on YY) must be strongly extensional.”

      because is not true. Assuming WLPO, Cantor space has decidable equality but the negation of equality is still not the tight apartness relation on Cantor space.

      Anonymouse

      diff, v4, current

    • For now creating page, more content to be added.

      v1, current

    • starting page on σ\sigma-complete Heyting algebras

      Anonymouse

      v1, current

    • New entry. This is a bit experimental. I will finish later. I want to add examples for instance the category of groups from the category of sets etc…

      v1, current

    • Precursor of a left adjoint, Borceux I.3.1.

      v1, current

    • added a Properties-section to pullback

    • Where does this concept come from? The page lists no relevant references, nor can I find any search results for “quadrable cospan”. Furthermore, the “Note on terminology” mentions the terminology “carrable”, which means something different as far as I can tell (and certainly in the cited references): namely, a morphism along which all pullbacks are admitted.

      diff, v8, current

    • These are notes that will gradually develop over the course of the next few months. The notes will be on many different topics of higher algebra and eventually merging in a representation theoretic direction (probably).

      Alexander Zahrer

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • There is a small error in the current proof that the category of endofunctors on a Q-category is a Q-category. I am going to correct it as soon as I find my way through the notation (I used it different on the paper). It now reads

      The (C R⊣C L)(C^R \dashv C^L)-unit is the dual C ηC^\eta of the original counit η\eta

      C η:Id C A→C L∘C R=C LR C^{\eta} : Id_{C^A} \to C^L \circ C^R = C^{L R}

      and the counit is the dual of the original unit

      C ε:C R∘C L=C RL→Id C A¯. C^\epsilon : C^R\circ C^L = C^{R L}\to Id_{C^{\bar{A}}} \,.

      The wrong thing is that C L∘C R=C RLC^L\circ C^R = C^{RL}, not C LRC^{LR} and that is why the unit and counit got interchanged; they should not get interchanged, but C LC^L and C RC^R should. I am going to sort this out. Thus C ηC^\eta where η\eta is unit goes C η:Id C A→C RLC^\eta : Id_{C^A}\to C^{RL}.

      Edit: the correct version is now below.

    • Explained the link between cliques of undirected simple graphs and coherence spaces.

      diff, v20, current

    • Change 1: Original page describes the fan theorem as requiring the bar to be decidable, claims that the “classical” fan theorem contradicts Brouwer’s continuity principle. The latter claim is not true; I corrected the error. I have stated the result as two separate theorems: the decidable fan theorem, about decidable bars, and the fan theorem, about bars in general.

      Change 2: Slightly more information is provided about the relationship between the Fan Theorem and Bar Induction. Eventually, we should make a page about the latter.

      Change 3: the section on equivalents to the fan theorem has been fixed somewhat. The section originally asserted that all of the statements provided were equivalent to the decidable fan theorem; in fact, some are equivalent to the decidable fan theorem and some to the full fan theorem.

      diff, v22, current

    • starting page on punctual cohesion

      Anonymouse

      v1, current

    • copied from HoTT wiki

      Anonymous

      v1, current

    • starting page on the axiom of sufficient cohesion

      Anonymouse

      v1, current

    • Added to BF-theory the reference that right now I am believing is the earliest one:

      Gary Horowitz, Exactly soluable diffeomorphism invariant theories Commun. Math. Phys. 125, 417-437 (1989)

      But maybe I am wrong. Does anyone have an earlier one? I saw pointers to A. Schwarz articles from the late 70s, but I am not sure if he really considered BF as such.

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

      v1, current

    • I added a little bit to maximal ideal (first, a first-order definition good for commutative rings, and second a remark on the notion of scheme, adding to what Urs wrote about closed points).

      The second bit is almost a question to myself: I don’t feel I really grok the notion of scheme (why it’s this and not something slightly different that’s the natural definition, the Tao if you like). In particular, it’s where fields – simple objects in the category of commutative rings – make their entrance in the notion of covering by affine opens that I don’t feel I really understand.

    • “for each nonzero element rr in a semiprimitive ring,…module left annihilated by rr.” to “…module not left annihilated by rr.”

      Anonymous

      diff, v7, current

    • Added:

      A survey of various notions between unital rings and nonunital rings:

      • Patrik Nystedt, A survey of s-unital and locally unital rings, Revista Integración, temas de matemáticas Escuela de Matemáticas, Universidad Industrial de Santander, Vol. 37, N◦ 2, 2019, pág. 251–260. doi.

      diff, v21, current

    • Trivial edit to start discussion.

      What’s happening at the start here? We have both tropical rig and semiring defined. The latter is given with the extension by {∞}\{\infty\}. Is this just duplication with a mistake?

      At semiring having given 4 definitions, it says

      The nLab uses the second definition to define a semiring, and the fourth definition to define a rig. The first and third are then called nonunital semirings and nonunital rigs respectively.

      Do we really have this as a policy?

      diff, v11, current

    • creating a separate page for semiring to accomodate diverging definitions of semirings in mathematics. The rig page should be left for discussing the particular semiring with additive and multiplicative identity elements.

      Anonymous

      v1, current

    • nonassociative groups: loops whose left and right inverses are the same

      Anonymous

      v1, current

    • Created Moufang loop and some links. It would be good to update the proof that the tangent bundle of a Lie group is trivial to include the case of the tangent bundle of a smooth Moufang loop.

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

      Anonymous

      v1, current

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

      Anonymous

      v1, current

    • quasigroups that are associative

      Anonymous

      v1, current

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

      Anonymous

      v1, current

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

      Anonymous

      v1, current

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