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

• Link to S5 and S4(m)

Ammar Husain

• 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.)

• changed title to match more systematic naming convention

• 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).

• renamed to full name

• splitting off this definition from neighborhood retract, for ease of linking, and in order to record the characterization AR = ANR+contractible

• expand with definition

• stub entry, for the moment just so as to record references

• 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

• table to be !include-ed for cross-linking into relevant entries

• touched the formatting of the pointers to references on characteristic of $E_\infty$-rings

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

mray

• 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.

• The individual morphisms $f_i$ are not usually faithfully flat – any faithfully flat morphism is surjective. I think they are also not quasicompact in general. See the definition of fpqc cover in the stacks project:

https://stacks.math.columbia.edu/tag/01K2

Anonymous

• 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?

• (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).

• Added information about weak enrichment in a bicategory. I put this in the idea section as well as the the definition section. I also added a reference. I’m sure there is a better reference out there but I couldn’t find one that is publicly available.