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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• starting some minimum

• I wanted to be able to use the link without it appearing in grey, so I created a stub for general relativity.

• I added to star-autonomous category a mention of “$\ast$-autonomous functors”.

• creating a minimum, so that the link works

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

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• starting something

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyerlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for yperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• now creating this entry.

The technical material under “Details” (here) is copied over from what I had written at reader monad – Examples – quantum reader monad. (There may still be room left to adjust the wording in order to reflect that this material moved to a new entry.)

To this I have now added an Idea-section (here) which highlights the relation to (equivalence with) Bob Coecke’s “classical structures” (which term I made redirect to here now)

• starting something, so far some paragraphs of an Idea-section (references to follow in a moment).

• brief category:people-entry for hyperlinking references

• created an entry modal type theory; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with monad (in computer science).

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• a bare list of references, to be !include-ed into the References-section of relevant entries (such as at braid group representation and at semi-metal).

Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited

• brief category:people-entry for hyperlinking references

• starting page for reference

• starting page for reference

• recorded some recent surveys of the status of MOND at MOND

• starting page for reference

Anonymous

• Fixing up the example of a piecewise defined function, which had extraneous notation, but also to introduce the vertically-stacked copairing notation mirroring the ’cases’-style layout of the usual piecewise definition

• Redirect: codiagonal map.

• In the examples section of extensive category, it is stated that the category of affine schemes is infinitary extensive.

For all I know, I was the one who stuck in that example. But is that statement actually true? I’m having trouble seeing it.

If $S$ is a commutative ring over $R$ (by which I mean under $R$ (-:), does the functor $S \otimes_R -: CAlg_R \to CAlg_R$ preserve arbitrary cartesian products? Because it seems that’s what we basically need for the statement to be true.

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

Anonymous

• a stub entry, for the moment just to record a couple of references

• I would like to include something on wheeled properads (or wheeled PROPs) in the nlab. It seems to me that a wheeled prop is something like a symmetric monoidal category with duals for every object generated by one object. Is this right? Is there a place in the litterature where i can find the relation between wheeled properads used by Merkulov and some kinds of symmetric monoidal categories with duality?

Before changing the PROP entry to add this variant, i would like to have a nice reference on this.
• I created a stub certified programming.

That’s motivated from me having expanded the Idea-section at type theory. I enjoyed writing the words “is used in industry”. There are not many $n$Lab pages where I can write these words.

I am saying this only half-jokingly. Somehow there is something deep going on.

Anyway, in (the maybe unlikely) case that somebody reading this here has lots of information about the use and relevance of certified programming in industry, I’d enjoy seeing more information added to that entry.

• I have expanded out the statement of (the ingredients of) the isomorphism a bit more and made explicit the statement of the relation to the Landweber exact functor theorem.

• updated link to my webpage

Also tried to fix the ordering of the rest of the reference, but I give up for the moment. This needs attention by some expert

• Updating reference to cubical type theory. This page need more work.

• brief category:people-entry for hyperlinking references

• I am moving the following old query box exchange from orbifold to here.

old query box discussion:

I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely does not view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.

Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?

end of old query box discussion

• Added a quotation as well as some references that point to the importance of Freudenthal in the advent of categorical concepts and terminology.

• I am finally creating this entry — meant as a bare list of hyperlinked terms to be !include-ed into the “Related concepts”-sections of the respective entries — for ease of synchronizing this list across all these entries.

(I am not sold on the title “mathematical statements”, it’s just the best I could come up with after a minute of thinking about it).

I am creating this now with the following list, but this may change as I now go through all the related entries:

• Added an Idea-section to this (previously stubby) entry — not meant to be definite, just what came to mind when finding that such a section was still lacking here:

In mathematics, a conjecture is a proposition which is expected to be true, hence expected to have a proof, but for which no proof is (currently) known.

Hence being a conjecture is a sociological aspect of a proposition, not a mathematical aspect: Once a proof (or else a counterexample) is found, the conjecture ceases to be a conjecture and instead becomes a theorem.

It happens that conjectures remain unproven while being perceived as trustworthy enough that further theorems are proven assuming the conjectures – in this case the conjecture plays the role of a hypothesis in the sense of formal logic.

For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).

In other cases the term “hypothesis” is used synonymously with “conjecture” – e.g. for the homotopy hypothesis (key cases of which have long become theorems) or the cobordism hypothesis (on which a proof has famously been claimed but not universally accepted).

• cross-linked with conjecture, adding these lines (following after the paragraph that starts out with “In formal logic…”):

In the practice of mathematics (or beyond), hypotheses that that are expected to have a proof, even if currently unknown, are known as conjectures.

For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).