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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
am finally splitting this off from Hopf degree theorem, to make the material easier to navigate. Still much room to improve this entry further (add an actual Idea-statement to the Idea-section, add more examples, etc.)
stub for dark matter
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).
I moved (n,k)-transformation to transfor, as seemed to be agreed upon by those who spoke up in the discussion there.
splitting off this definition from neighborhood retract, for ease of linking, and in order to record the characterization AR = ANR+contractible
Somebody sent me an email with the following comment on the entry countable set. I am not in position to react to this, maybe some expert here could reply. The sentence being quoted originates from revision 1 of the entry.
Forwarded message:
“We do have, however, that a countable set is either empty or inhabited, which is classically trivial but need not hold constructively for every set.”
(https://ncatlab.org/nlab/show/countable+set)
The set D={n\in N | 2n+6 is not the sum of two odd primes} is decidable, hence countable. However we cannot decide whether it is empty or inhabited. (We could decide it if we assumed LPO, for instance.)
Do you agree?
Created an article for DisCoCat (which is a major industry in the Oxford Quantum Group), plus an incoming link from linguistics
brief category:people-entry for hyperlinking references at cohomotopy and at equivariant Tietze extension theorem
Made a start on this at orthogonal subcategory problem. There should be much more to say about this with regard to various generalities in model category theory. Needs some clean-up. Please have a look.
added to symmetric monoidal category a new Properties-section As models for connective spectra with remarks on the theorems by Thomason and Mandell.
There has GOT to be a better photograph than that! Is there anyone here in Oxford? Can they go and get a picture for us?
this MO comment made me realize that we didn’t have an entry proof assistant, so I started one
(Hi, I’m new)
I added some examples relating too simple to be simple to the idea of unbiased definitions. The point is that we often define things to be simple whenever they are not a non-trivial (co)product of two objects, and we can extend this definition to cover the “to simple to be simple case” by removing the word “two”. The trivial object is often the empty (co)product. If we had been using an unbiased definition we would have automatically covered this case from the beginning.
I also noticed that the page about the empty space referred to the naive definition of connectedness as being
“a space is connected if it cannot be partitioned into disjoint nonempty open subsets”
but this misses out the word “two” and so is accidentally giving the sophisticated definition! I’ve now corrected it to make it wrong (as it were).
created a stub for holographic entanglement entropy in reaction to this MO question.
stub for toric variety