Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
started an entry geometric realization of simplicial topological spaces.
I decided this is a topic big enough to justify splitting it off from geometric realization (of simplicial sets).
But not much there yet. I just wanted to record for the moment that this realization too, does preserve pullbacks.
have split off semi-simplicial object from semi-simplicial set.
At our workshop yesterday we heard Dominic Orchard speak about “Graded Modal Logic for Linear Dependent Type Theory”/ So I’ve started graded modality.
Now any connection to Licata-Shulman-Riley?
stub for equivariant elliptic cohomology, for the moment just to record the references given there
added graphics of the light hadron masses from Fodor-Hoelbling 12
I have split off bisimplicial set and bisimplicial group from bisimplicial object
created at internal logic an Examples-subsection and spelled out at Internal logic in Set how by turning the abstract-nonsense crank on the topos Set, one does reproduce the standard logic.
Created:
Analytic monads are monads on Set that correspond to operads in Set.
More precisely, an operad in Set induced a monad on Set:
Such a monad is equipped with a canonical weakly cartesian natural transformation to the moand arising from the commutative operad.
A theorem of Joyal \cite{Joyal} states that there is a monoidal equivalence between the monoidal category of endofunctors that admits a weakly cartesian natural transformation to and the monoidal category of species, i.e., symmetric sequences in Set with the substitution product.
In particular, the category of analytic monads on Set is equivalent to the category of operads in Set.
The correspondence carries over to colored operads (with a set of colors ) if we use the slice category instead of Set.
A similar correspondence can be established for nonsymmetric case, except that we must include the data of a transformation to , which is no longer unique.
The correspondence generalizes to (∞,1)-categories, with some statements becoming more elegant. See Gepner–Haugseng–Kock \cite{GHK}.
André Joyal, Foncteurs analytiques et espèces de structures, Combinatoire énumérative (Montréal/Québec, 1985), Lecture Notes in Mathematics 1234 (1986), 126-159. doi.
Mark Weber, Generic morphisms, parametric representations and weakly Cartesian monads, Theory Appl. Categ. 13 (2004), 191–234.
David Gepner, Rune Haugseng, Joachim Kock, ∞-Operads as Analytic Monads, arXiv:1712.06469.
the entry braid group said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).
created worldline formalism to go with this Physics.SE answer
I’ve added Peter May’s Galois theory example to M-category in a section “Applications”.
Created:
A book by Tom Leinster.
London Mathematical Society Lecture Note Series 298 (2004).
Cambridge University Press.
ISBN 0 521 53215 9.
added pointer to Bredon 72. Will add this pointer also to various related entries on equivariant homotopy theory
started Lie algebra cohomology,
(for the moment mainly to record that reference on super Lie algebra cocycles)
following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.
Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.
started a Properties-section at Lawvere theory with some basic propositions.
Would be thankful if some experts looked over this.
Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.
I’ve added a definition to locally cartesian closed model category, although I’m open to debate about whether this is the right definition. This definition is more or less exactly what one needs to interpret dependent products in type theory with function extensionality (I plan to add a proof of this). But it’s certainly less obviously correct from a pure model-categorical viewpoint. For one thing, it doesn’t imply that we have a cartesian closed model category, which one would naively expect a notion of “locally cartesian closed model category” to do.
polished and expanded adjoint (infinity,1)-functor
it seems we were lacking an entry completion of a ring. I started a bare minimum and cross-linked with p-adic integers and localization of a ring. Wanted to do more, but am being interrupted now.
stub for Atiyah-Segal completion theorem, for the moment just to record a reference
added to representation ring a brief remark on its relation to the equivariant K-theory of the point (very stubby still)
Am making a start on trying to understand something of Mochizuki’s IUTT papers. I do not hold out any promises on how far I am going to get, or how long it is going to take me! Even this very first definition is going to me a long time, I think, as I intend to try to fill out all details. All help will be appreciated!
I have changed the title of this article, as well as references to the object within it. Use of the term “Hawaiian Earring” is objected to by Hawaiian mathematicians. Please see these two threads, one by native Hawaiian and math PhD Dr. Marissa Loving, and the other by an expert on the Hawaiian Earring, Dr. Jeremy Brazas.
https://twitter.com/MarissaKawehi/status/1406244897611522049
https://twitter.com/jtbrazas/status/1406652385263501319
I have retitled the article “Shrinking wedge of circles”, which is the name used for this space in Hatcher’s “Algebraic Topology”. I have a retained a note in the body of the article that the space is sometimes referred to as the “Hawaiian earring space”.
This small change in name helps to make mathematics a more inclusive and just field, especially in consideration of the historical marginalization and exclusion of indigenous mathematicians. By taking this action, the nLab site can help to spread a change in language more widely, including on other math reference sites.
I hope that this change is readily accepted and approved by the nLab community. Thank you!
Justin Lanier
a bare list of references, to be !include-ed into relevant entries, such as at elliptic cohomology, but also at equivariant elliptic cohomology, elliptic genus, Witten genus etc.
(in an attempt to clean up and harmonize the referencing across all these entries – still some way to go towards that goal, but it should be a start)
added a tiny bit of basics to complex oriented cohomology theory
just to make links work, I have started a minimum at gravitational wave.
Stub. For the moment just for providing a place to record this reference:
I understood that the old terminology was ’projective system’, and ’projective limit’ refereed to the limit of a projective system. Can anyone confirm that? if I am right the present entry is slightly incorrect, but this needs checking first before changing it.
I edited the formatting of internal category a bit and added a link to internal infinity-groupoid
it looks like the first query box discussion there has been resolved. Maybe we can remove that box now?
brief category:people-entry for hyperlinking references at FGA explained and elsewhere
brief category:people-entry for hyperlinking references at FGA explained, and elsewhere
I updated a link on FGA explained to one of the chapters, to point to the arXiv version (the one on constructing Hilbert and Quot schemes). I also added a link to the conference page itself, which has links to scans of lecture notes, as the direct lecture notes links seem to be broken.
Wrote a minimum of substance to this entry. My interest is prompted by current thinking on -dimensional analogues of Euler angles. There are several articles (mainly in quantum chemistry and mathematical physics literature) around 1969-1974, which introduce some analogues via calculational procedures. In my taste an elementary geometrical introduction using both intrinsic and extrinsic approach, in a spirit of Euler, will be more suggestive.
added to simplicial object a section on the canonical simplicial enrichment and tensoring of for having colimits and limits.
Some tidying up and additions at simplex category, in particular a section on its 2-categorical structure, and more on universal properties.
I’ve edited the definition to focus more on the augmented simplex category instead of the ’topologists’ ’, but I haven’t changed their names, because it seemed to me that that was the best way to keep everyone involved in the discussion at that page happy. (I also changed the ordinal sum functor from to , after Tim’s suggestion.)
Added a reference of Robert Furber, Bart Jacobs at Giry monad.
Created Gamma-space.