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    • Removed a query box:

      Tim: These are called derivations by some sources, but I think that they are the coderivations of other workers. (to be checked)

      diff, v18, current

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

      Anonymous

      v1, current

    • I gave the stub-entry Hopf algebroid a paragraph in the Idea-section that points out that already in commutative geometry there are two different kinds of Hopf algebroids associated with a groupoid (just as there are two versions of Hopf algebras associated with a group):

      1. The commutative but non-co-commutative structure obtained by forming ordinary function algebras on objects and morphisms;

      2. The non-commutative but co-commutative structure obtained by forming the groupoid convolution algebra.

      For the moment I left the rest of the entry (which vaguely mentions commutative and non-commutative versions without putting them in relation) untouched, but I labelled the whole entry “under constructions”, since I think this issue needs to be discussed more for the entry not to be misleading.

      I may find time to get back to this later…

    • this article needs a lot of improvement. I did some basic things like adding section headers, a table of contents, a related concepts section, references, and redirects for the plural

      type theorist

      diff, v3, current

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

      Anonymous

      v1, current

    • I just have met Jamie Vicary in Brussels, at QPL 2012. In his nice talk he pointed to an nnLab page which I didn’t know existed:

      It’s about a computer algebra software that can handle KV-2-vector spaces. I have just now added some cross links.

    • added English translation of this bit

      PN§260 Der Raum ist in sich selbst der Widerspruch des gleichgültigen Auseinanderseins und der unterschiedlosen Kontinuität, die reine Negativität seiner selbst und das Übergehen zunächst in die Zeit. Ebenso ist die Zeit, da deren in Eins zusammengehaltene entgegengesetzte Momente sich unmittelbar aufheben, das unmittelbare Zusammenfallen in die Indifferenz, in das ununterschiedene Außereinander oder den Raum.

      Space is in itself the contradiction of the indifferent being-apart and of the difference-less continuity, the pure negativity of itself and the transformation, first of all, to time. In the same manner time – since its opposite moments, held together in unity, immeditely sublate themselves – is the undifferentiated being-apart or: space.

      And polished a little around and following this bit.

      diff, v269, current

    • added to Mizar a quote:

      Naumowicz 06:

      One of the biggest problems that worry the developers of automated deduction systems is that their systems are not sufficiently recognized and exploited by working mathematicians. Unlike the computer algebra systems, the use of which has indeed become ubiquitous in the work of mathematicians these days, deduction systems are still seldom used. They are mostly used to formalize proofs of well-established and widely known classical theorems, the Fundamental Theorem of Algebra formalized in the systems Coq and Mizar may serve as a perfect example here. Such work, however, is not always considered to be really challenging from the viewpoint of mathematicians who are concerned with obtaining their own new results. Therefore it has been recognized as a big challenge for the deduction systems community to prove that some of the state-of-the-art systems are developed enough to cope with formalizing recent mathematics.

    • changed link for gitit from gitit.net (a yale group not related to this page) to the github page for gitit.

      mray

      diff, v14, current

    • added references to Lean

    • I have created a page list of mathematics software with links to all the nLab pages I could find about software packages, and put all of those pages in category: software.

    • starting page on dependent type theory with type variables

      Anonymouse

      v1, current

    • I think we should expand this list of languages!

      Anonymous

      diff, v16, current

    • starting page on record types

      Anonymouse

      v1, current

    • This is the list from proof assistant – Examples, and was (incompleteky) copied by hand into related entries, but we should make it (as done hereby) a standalone to be !includeed under “Related concepts” in relevant entries

      All I did in editing was to group the proof assistants into “based on type/set theory” and “applicable to homotopy type theory”. Experts please hit “edit” and improve on it

      v1, current

    • starting disambiguation page on impredicative universes

      Anonymouse

      v1, current

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

      Anonymous

      v1, current

    • propositional impredicativity of universes, not to be confused with propositional resizing

      Karl Schoenbaum

      v1, current

    • Have added to HowTo a description for how to label equations

      In the course of this I restructured the section “How to make links to subsections of a page” by giving it a few descriptively-titled subsections.

    • I was just made aware of writing in the nLab by Todd Trimble on the category theory Zulip. I think this article should be updated to the current state of the nLab in 2025 (e.g. remark 1.1 should be removed because it isn’t true anymore). It should also be linked from the first section of the HomePage so that users have an idea what to do and what not to do on the nLab. I believe if it was accessible from the HomePage all these years, then we wouldn’t have had so many anonymous editors posting their original research on the nLab in the past few years.

    • starting disambiguation page on skeleton in mathematics

      v1, current

    • corrected the reference to point to the right publication

      diff, v4, current

    • apartness relation says

      The negation of an apartness relation is an equivalence relation. (The converse of this is equivalent to excluded middle.)

      But it seems to me that the converse (“the negation of an equivalence relation is an apartness relation”) only requires de Morgan’s law. If ≈\approx is an equivalence relation, then certainly ¬¬(x≈x)\neg\neg(x\approx x) and ¬(x≈y)→¬(y≈x)\neg (x\approx y) \to \neg(y\approx x), so the only thing to worry about is comparison. If ¬(x≈z)\neg (x\approx z), then contraposing transitivity gives ¬(x≈y∧y≈z)\neg (x\approx y \wedge y\approx z), which by de Morgan gives ¬(x≈y)∨¬(y≈z)\neg (x\approx y) \vee \neg (y\approx z).

    • Test edit, I can’t seem to get the page to accept the larger edit I’ve made.

      diff, v26, current

    • Entry to fill in some of the ideas from a poset viewpoint. Note the use of the term ’residual’ for the left adjoint. It seems that this use is really traditional coming from the sense that a ’residue’ is the bit left ove. The link with ‘internal homs’ is then a categorication of that, which puts a different light on internal homs!

      v1, current

    • Page to complete stubs on residuated things (more could be added).

      v1, current

    • starting page on idempotent monoids

      v1, current

    • starting page on additively idempotent rigs for rigs whose addition is idempotent

      v1, current

    • starting disambiguation page on idempotent rigs

      v1, current

    • Added as examples: 00, ℤ/2ℤ\mathbb{Z}/2\mathbb{Z} and 𝔹={0,1}\mathbb{B}=\{0,1\} with 1+1=01+1=0. Proved that they are exactly the boolean rigs of cardinal less or equal than 22.

      I don’t know if boolean rigs in the sense of this entry are always commutative. In The variety of Boolean semirings, they show that they are commutative assuming that 1+x+x=11+x+x=1. If some noncommutative boolean rig exists, it must be of cardinal ≥3\ge 3, not be a ring (because boolean rings are commutative) and not verify this equation.

      diff, v6, current

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

      diff, v5, current

    • Added link to “multiplicatively cancellable semi-ring”.

      diff, v32, current

    • starting page on Boolean semirings as defined by Fernando Guzmán

      v1, current

    • starting page on Boolean semirings as defined in the literature

      v1, current

    • starting page on disambiguation page

      v1, current

    • Note that indeed any idempotent magma in AbAb is commutative.

      diff, v10, current

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