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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added at core the remark that the core is right adjoint to the forgetful functor Grpd→Cat.
The Idea-section at quasi-Hopf algebra had been confused and wrong. I have removed it and written a new one.
Adding reference
Anonymous
Have added pointer to:
(but I haven’t more than skimmed it and don’t mean to endorse it).
Stub to record today’s reference
- Bhargav Bhatt, Peter Scholze, Prisms and Prismatic Cohomology, preprint (2019) arXiv:1905.08229
moving section on the antithesis interpretation in linear logic to its own page at antithesis interpretation
Anonymouse
Started something to record today’s article
a bare list of references, to be !include-ed into the References-sections of relevant entries (such as at supergeometry and fermion), for ease of synchronization
Create a page for this theorem (mostly copied the text from initial algebra of an endofunctor).
I have incorporated Jonas’ comment into the text at pretopos, changing the definition to “a category that is both exact and extensive”, as this is sufficient to imply that it is both regular and coherent.
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?
The pages apartness relation and antisubalgebra disagree about the definition of an antiideal: do we assume ¬(0∈A) or ∀p∈A,p#0? Presumably there is a similar question for antisubgroups, etc. In particular, the general universal-algebraic definition at antisubalgebra would give ¬(0∈A) as the definition (since 0 is a constant and ⊥ is a nullary disjunction), contradicting the explicit definition of antiideal later on the same page.
Does this have something to do with whether #-openness is assumed explicitly or not? The page apartness relation claims that, at least for antiideals, openness is automatic as long as the ring operations are strongly extensional. But antisubalgebra assumes openness explicitly, in addition to strong extensionality of the algebraic operations.
Finally, do we ever really need the apartness to be tight?
A method in integrable systems.
FRT approach to quantum groups
New pages quantum linear group, quantized function algebra (redirects also quantized coordinate ring) and quantized enveloping algebra which refer to certain special cases of a general family of notions of quantum group.
one more from Meissner & Nicolai, last week:
I have expanded the Idea-section at deformation quantization a little, and moved parts of the previous material there to the Properties-section.
I think the second sentence below needs to have the phrase “torsion-free” added to it twice. Right? I’m going to do that.
a) The category λRing of λ-rings is monadic and comonadic over the category of CRing of commutative rings.
b) The category λRing¬tor of λ-rings is monadic and comonadic over the category of CRing¬tor of commutative rings.
added reference to dendroidal version of Dold-Kan correspondence
Stub a page for what has been called “the most important law”, “the only unbreakable law”, and a generalization of both Amdahl’s and Brooks’ laws. While this is important to software engineering, it’s applicable to any engineered system, and Conway 1968 uses all sorts of infrastructure to make their point alongside software-specific examples.
Have added to cyclic set a pointer to notes from 1996 by Ieke Moerdijk where the theory classified by the topos of cyclic sets is identified (abstract circles).
This is an unpublished note, but on request I have now uploaded it to the nLab
I have also added a corresponding brief section to classifying topos.
By the way, there is an old query box with an exchange between Mike and Zoran at cyclic set. It seems to me that this has been resolved and the query box could be removed (to make the entry read more smoothly). Maybe Mike and/or Zoran could briefly look into this.
have added pointers to Alex Hoffnung’s preprint to tetracategory, tricategory, span and (infinity,n)-category of spans.
Created a stub for this concept, as I think it’s important to distinguish between coherence theorems and strictification theorems, as, while they are related, they are not the same, and their relationship can be quite subtle. I plan to expand this page and move some content over from coherence theorem soon.
added an Idea-section to coherence theorem for monoidal categories just with the evident link-backs and only such as to provide a minimum of an opening of the entry
added to gravity references discussing the covariant phase space of gravity, as part of a reply to this TP.SE-question