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

• Changed localy to locally

Anonymous

• Fixed typo in Definitions section

Anthony Hart

• Added to paracompact topological space in the Properties-section the statement that every bounded hypercover over a paracompact space is refined by the Čech nerve of a plain open cover… by appealing to a lemma in HTT. (Thanks to Danny Stevenson for pointing this out.)

• Mention connection with normal covers.

• I added a bit to category of simplices, including the fact that the category of nondegenerate simplices is final and thus colimits can be computed using only that, and that the nerve of the category of simplices itself is colimit-preserving.

• fixed the formatting of the reference itself. Also the toc formatting needs fixing (what was the intention here, is this a copy-and-paste artefact?), but my battery dies now and I’ll leave it at that

• trying to collect references on the state-of-the-art of computer simiulations on cosmic structure formations. Will try to expand as I find more…

• added some more keywords to the “index” (came here to add action object, but added a few more while I was at it)

• a plain list of hyper-linked keywords, to serve as floating context menu for relevant entries

(prodded by discussion here)

• starting something, to be another item of internalization along with monoid object and group object.

Not done yet, but need to save.

(Our entry “action” does cover internal notions of actions, but it seems hard to bring that old entry into a good shape, and in any case splitting off an entry on the internal notion might just be the first step of bringing it into shape)

The evident question for compiling this entry is: What are the canonical original references?

Eckmann-Hilton in their articles originally introducing the notion of internal group objects (here) have all the ingredients in hand to say “action object”, but it seems they don’t (?).

I found the notion stated clearly and explicitly, albeit somewhat in passing, in:

but if anyone has other/better references, let’s add them.

• I have edited at HQFT, touched the general formatting and structuring a good bit, trying to clean it up and beautify it a bit, and added a brief cross-pointer to the cobordisms hypothesis for cobordisms with maps into a base manifold.

• am splitting this off from holographic QCD, since the latter is getting too crowded. Prompted by today’s

• this is a bare list of references, to be !include-ed as a subsection in the References-sections of relevant entries

• I added an explicit definition of cartesian model category to cartesian closed model category to highlight the convention that the terminal object is assumed cofibrant.

• Generalize to higher-order polynomials

• I noticed that there was no entry quotient stack, so I quickly started one, just to be able to point to it from elswhere.

• added to Eckmann-Hilton argument the formal proposition formulated in any 2-category.

BTW, doesn’t anyone have a gif with the nice picture proof?

• Created.

• I pasted in something Mike wrote on sketches and accessible models to sketch. But now it needs tidying up, and I’m wondering if it might have been better placed at accessible category. Alternatively we start a new page on sketch-theoretic model theory. Ideas?

• a bare list of entries, to be !include-ed in lists of “Related entries”, for ease of cross-linking

• Replaced Monoid_mult.png to LaTeX contents.

• Adding a few more examples

Anonymous

• two-valued objects are topos-theoretic analogues of the set $\mathbf{2}$ with two elements in $Set$, and the categorical semantics of the type of booleans. Different from subobject classifiers. Still to do: categorical semantics of binary coproduct types and binary product types using dependent sums and products and two-valued objects.

Anonymous

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

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

• a stub, just for completeness

• The type with two elements, or homotopically the zero-dimensional sphere.

Anonymous

• Starting something, prompted by discussion here.

• felt like archiving a quote by Paul Taylor somewhere, it is now at folklore.

Besides being funny, it is actually a useful comment for the newbie, and so I linked to it from category theory.

• I rephrased and restructured the Definition-section at join of simplicial sets a bit, in an attempt to make the exposition clearer. Please check if I succeeded.

• I had started an entry “exponentiation” but then thought better of it and instead expanded the existing exponential object: added an examples-section specifically for $Set$ and made some remarks on exponentiation of numbers.

• Added Rainer Vogt’s file as a reference here as well.

• Created.

• Created.

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• Created.

• I have split off an entry classical model structure on simplicial sets from “model structure on simplicial set”. This entry should eventually contain detailed, self-contained and polished discussion of the definition, verification and key properties of the standard Kan-Quillen model structure.

So far I have inserted fair bit of background material regarding (minimal) fibrations and geometric realizations, essentially the material in chapter 1 of Goerss-Jardine. A bunch of little proofs are spelled out, but not yet the more laborious ones. Discussion of the verification of the axioms is not yet in the entry, but the key parts of the Quillen equivalence to $Top_{Quillen}$ are (modulo relying on previous lemmas that don’t have proofs spelled out yet).

The somewhat random list of properties of $sSet_{Quillen}$ that used to be sitting at “model structure on simplicial sets” I have copied over to a section “Basic properties”, just for completenes, but this now needs re-organization to give decent logical flow.

For the moment I have to leave it at that, need to take care of something else now for a little bit.

• Disambiguated the article, moved some content to polytope.

• some minimum, in order to make the link work

• starting something. Not much here yet besides the definition, but need to save.

• Several recent updates to literature at philosophy, the latest being

• Mikhail Gromov, Ergostructures, Ergologic and the Universal Learning Problem: Chapters 1, 2., pdf; Structures, Learning and Ergosystems: Chapters 1-4, 6 (2011) pdf

which is more into cognition and language problem, but still very relevant, and by a top mathematician. As these 2 are still manuscripts I put them under articles, though I should eventually classify those as books…