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A generalization of Waldhausen K-theory to dualizable dg-categories and dualizable stable ∞-categories.
For compactly generated inputs, recovers the Waldhausen K-theory of the full subcategory of compact objects.
The formalism is applicable to -presentable stable ∞-categories, where can be uncountable (for example, various categories of sheaves, or categories occurring in functional analysis).
Alexander Efimov, On the K-theory of large triangulated categories, ICM 2022, https://www.youtube.com/watch?v=RUDeLo9JTro
Marc Hoyois, K-theory of dualizable categories (after A. Efimov), https://hoyois.app.uni-regensburg.de/papers/efimov.pdf.
Li He, Efimov K-theory and universal localizing invariant, arXiv:2302.13052.
I reorganized linearly distributive category by moving the long block of history down to the bottom, adding an “Idea” section and a description of how -autonomous categories give rise to linearly distributive ones and linearly distributive ones give rise to polycategories. I also cross-linked the page better with polycategory and star-autonomous category.
started topologically twisted D=4 super Yang-Mills theory, in order to finally write a reply to that MO question we were talking about. But am being interrupted now…
I added some material to Peano arithmetic and Robinson arithmetic. At the latter, I replaced the word “fragment” (which sounds off to my ears – actually Wikipedia talks about thisterm a little) with “weakening”.
Still some links to be inserted.
added some minimum of content to this stub entry, including pointer to today’s
added pointer to yesterday’s
completed publication data for:
a bare list of references, to be !include
-ed into the References-sections of relevant entries (such as as Cartan structural equations, Bianchi identities, Cartan connection etc.)
added this quote to before the Idea-section:
In the wake of the movement of ideas which followed the general theory of relativity, I was led to introduce the notion of new geometries, more general than Riemannian geometry, and playing with respect to the different Klein geometries the same role as the Riemannian geometries play with respect to Euclidean space. The vast synthesis that I realized in this way depends of course on the ideas of Klein formulated in his celebrated Erlangen programme while at the same time going far beyond it since it includes Riemannian geometry, which had formed a completely isolated branch of geometry, within the compass of a very general scheme in which the notion of group still plays a fundamental role.
[Élie Cartan 1939, as quoted in Sharpe 1997, p. 171]
have expanded the single sentence at differential geometry to something like a paragraph, indicating how differential geometry is the “higher geometry modeled on the pre-geometry ”
a bare list of references, previously coded both at D=11 supergravity and at higher curvature correction, now extracted here to be !include
-ed back there, for ease of synchronizing
added a bunch of pointers to the literature (with brief comments) at string scattering amplitude.
Also added a corresponding paragraph at effective field theory.
(this is still in reaction to that MO discussion, specifically to the question here)
a bare list of references, to be !include
-ed into relevant entries (such as Witten genus, M5-brane elliptic genus but also inside elliptic cohomology – references) – for ease of harmonizing lists of references
added pointer to:
Created in context of topology - global countability axioms
Created page for BSU(n), the classifying space of the special unitary group SU(n). (See discussion on Stiefel-Whitney class.) There’s still a lot to add, but I will do so in the future. (The english and german Wikipedia page are now also available.)
Created page for BSO(n), the classifying space of the special orthogonal group SO(n). (See discussion on Stiefel-Whitney class.) There’s still a lot to add, but I will do so in the future. (The english and german Wikipedia page are now also available.)
Created ternary frame, a class of models for substructural logic which are basically obtained from Day convolution for promonoidal posets. Presumably people who know things know this, but in a few minutes of looking I haven’t found anyone mentioning it. Girard’s “phase space” semantics for linear logic (no relation to phase spaces of physics) are just the special case of regarding a monoidal category as a promonoidal one.
stub for braid group statistics (again, for the moment mainly in order to record a reference)
Creating the page, linked to from isofibration currently. Not yet finished, but contains so far the definition and some remarks on expressing it as a lifting condition. In a later edit, I will discuss the second condition, and remark on viewing Lack fibrations as ’Hurewicz fibrations’.
stub for S-duality – disambiguation and then the physics meaning
added references to essentially algebraic theory. Also equipped the text with a few more hyperlinks.
gave torsion of a Cartan connection its own entry, and cross-linked a bit.
added this pointer:
a stub, for the moment just so as to record pointer to Simpson 12 where “resolution of the paradox” is claimed to be achieved simply by passing from topological spaces to locales
wrote a definition and short discussion of covariant derivative in the spirit of oo-Chern-Weil theory
added pointer to:
Created an entry for this.
I’ve adopted the existing convention at nLab in the definition of (which is also the definition I prefer).
Since the opposite convention is used a lot (e.g. by Lurie), I’ve decided it was worth giving it notation, the relation between the versions, and citing results in both forms. Since I didn’t have any better ideas, I’ve settled on .
I just added a link to Lurie's "What is...?" paper.
added more publication data and links to:
also, I have fixed the order of the editor’s names
Created page for BU(n), the classifying space of the unitary group U(n). (See discussion on Stiefel-Whitney class.) There is still a lot to add though.
Created page for BO(n), the classifying space of the orthogonal group O(n). (See discussion on Stiefel-Whitney class.) There is still a lot to add though.
added to S-matrix a useful historical comment by Ron Maimon (see there for citation)