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

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    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Changed requiring that all j-morphisms are invertible to demand being equivalences as in infinity-groupoid entry.

      diff, v10, current

    • Created a small page to describe the different usages of the term locally.

      v1, current

    • Changed simplicial algebra for cosimplicial algebra (affine stacks are Spec of cosimplicial cdgas).


      diff, v54, current

    • Created a stub with a definition.

      v1, current

    • Added alternative terminology “local right adjoint” and “strongly cartesian monad” from Berger-Mellies-Weber. They claim the former “has become the more accepted terminology” than “parametric right adjoint”; does anyone know other references to support this? (I think it’s certainly more logical, in that it fits with the general principle of “local” meaning “on slice categories” — not to be confused with the different general principle of “local” meaning “in hom-objects”.)

      diff, v8, current

    • Stub. For the moment just for providing a place to record this reference:

      • Jean Thierry-Mieg, Connections between physics, mathematics and deep learning, Letters in High Energy Physics, vol 2 no 3 (2019) (doi:10.31526/lhep.3.2019.110)

      v1, current

    • I have removed the following discussion box from stuff, structure, property – because the entry text above it no longer contained the word that the discussion is about :-)

      [begin forwarded discussion]

      +–{: .query} Mike: Maybe you all had this out somewhere that I haven’t read, but in the English I am accustomed to speak, “property” is not a mass noun. So you can “forget a property” or “forget properties” but you can’t “forget property.”

      Toby: Well, ’property’ can be a mass noun in English, but not in this sense. Also, if we were to invent an entirely new word for the concept, it would surely be a mass noun. Together, these may explain why it's easy to slip into talking this way, but I agree that it's probably better to use the plural count noun here. =–

      [end forwarded discussion]

    • starting something. Not done yet but need to save

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I felt like the (∞,1) section should give an abstract description rather than a model specific one, so I’ve done so, and proved in the abstract the equivalence between the hom-space and slice-category characterizations.

      It feels like cheating to invoke the Grothendieck construction for it; can the argument be made just as cleanly without it?

      … I’m having trouble with the formatting, so I’m going to do some bisection to track down the issue….

      diff, v38, current

    • I have expanded the Idea section in localization of model categories as it previously seemed to be a stub. (It said: A localisation for model categories. Doh!) I have given a quote from Hirschhorn’s book.

    • Created a stub for nuclear adjunctions.

      v1, current

    • started working on superalgebra. But have to interrupt now.

    • added to Yang-Mills instanton a discussion of instantons as tunnelings between Chern-Simons vacua.

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I was a bit confused about a search for “pullback lemma” not returning any result, hence this redirect

      diff, v7, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • for completeness in view of the other real normed division algebras, I added statement of the automorphism group

      diff, v25, current

    • the entry Galois theory used to be a stub with only some links. I have now added plenty of details.

    • I corrected an apparent typo:

      A 2-monad TT as above is lax-idempotent if and only if for any TT-algebra a:TAAa \colon T A \to A there is a 2-cell θ a:1ηa\theta_a \colon 1 \Rightarrow \eta \circ a


      A 2-monad TT as above is lax-idempotent if and only if for any TT-algebra a:TAAa \colon T A \to A there is a 2-cell θ a:1η Aa\theta_a \colon 1 \Rightarrow \eta_A \circ a

      It might be nice to say η A\eta_A is the unit of the algebra….

      diff, v22, current

    • Started this page to record various facts about large cocompletions as I survey some of the literature. It’s possible that some of these concepts should have their own pages eventually, but at the moment this seems awkward as many don’t already have names in the literature (or have names that are not ideal for various reasons).

      v1, current

    • added pointer to the entries on Wikipedia and on MathGenealogy

      and added a couple of items under “Selected writings”

      diff, v3, current


      Suggests that Stone, Gelfand, … duality are special cases of the adjunction between CoPresheaves and Presheaves. A similar question is raised here.

      However, this paper

      seems to use another definition. Could someone please clarify?

    • It didn’t seem we had a page for this, and yet it seems notable enough to warrant one, mainly for cross-linking purposes.

      v1, current

    • Added TAC’s subpublications: Reprints and Expositions.

      diff, v11, current

    • How would people feel about renaming distributor to profunctor? I seem to recall that when this came up on the Cafe, I was the main proponent of the former over the latter, and I've since changed my mind.

    • I added some material to Mal’cev variety, namely proofs showing the various characterizations are equivalent, and a brief Examples section.

    • all of

        [[!redirects coreflector]]
        [[!redirects coreflectors]]
        [[!redirects coreflection]]
        [[!redirects coreflections]]
        [[!redirects coreflective subcategory]]
        [[!redirects coreflective subcategories]]

      used to still be in reflective subcategory. I have removed it there and instead included these redirects here

      diff, v16, current

    • Created arity class. Added links from a few places, but there are probably others I didn’t think of.

    • added pointer to

      • Tom Lovering, Etale cohomology and Galois Representations, 2012 (pdf)

      for review of how Galois representations are arithmetic incarnations of local systems/flat connections. Added the same also to local system and maybe elsewhere.

    • added references to Lean

    • brief category:people-entry for hyperlinking references

      v1, current

    • added to generalized Reedy category a bunch of definitions and propositions from Cisinski’s article, concerning the notion of normal morphisms of presheaves over a generalized Reedy category.

    • tried to polish one-point compactification. I think in the process I actually corrected it, too. Please somebody have a close look.

    • added to modality a minimum of pointers to the meaning in philosophy (Kant).

    • Added a reference.

      Can we say exactly what kind of pretopos the category of small presheaves on a category C is?

      Is it a ΠW-pretopos, provided that PC is complete?

      diff, v9, current

    • Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).

    • I fixed a trivial typo in adjoint functor theorem but left wondering about this:

      … the limit

      Lc:=lim cRdd L c := \lim_{c\to R d} d

      over the comma category c/Rc/R (whose objects are pairs (d,f:cRd)(d,f:c\to R d) and whose morphisms are arrows ddd\to d' in DD making the obvious triangle commute in CC) of the projection functor

      Lc=lim (c/RD). L c = \lim_{\leftarrow} (c/R \to D ) \,.

      I don’t really understand this (and while I could figure it out, it’s probably not good to make readers do so). At first it sounds like someone is saying “the limit LcL c over the comma category of the projection functor LcL c”, which would be circular. But it must be that both formulas are intended as synonymous definitions of LcL c. At that point one is left wondering why one has a backwards arrow under it and the other does not. I guess old-fashioned people prefer writing limits with backwards arrows under them, so someone is trying to cater to all tastes? I think it’s better in this website to use limlim and colimcolim for limit and colimit.

      I could probably guess how to fix this, but I won’t since I might screw something up.

    • brief category:people-entry for hyperlinking references

      v1, current