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    • Added remark on geometric realizations of pairs of adjoint functors

      Roman T

      diff, v17, current

    • some minimum, for the moment just to address the issue raised in another thread, here

      v1, current

    • starting a category:reference-page in which to eventually collect pointers to the contributions to this upcoming book collection

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • We may be hearing next week about the internal logic of (∞,2)(\infty, 2)-toposes. Is there anything to say further on this page beyond what we find out at 2-topos?

      diff, v7, current

    • Started something to record today’s article

      • David Kern, Categorical spectra as pointed (∞,ℤ)(\infty,\mathbb{Z})-categories [arXiv:2410.02578]

      v1, current

    • 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

      v1, current

    • Mike Stay kindly added the standard QM story to path integral.

      I changed the section titles a bit and added the reference to the Baer-Pfaeffle article on the QM path integral. Probably the best reference there is on this matter.

    • Page created, but author did not leave any comments.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • 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

    • 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.

    • creating an entry with just a bare minimum

      v1, current

    • The pages apartness relation and antisubalgebra disagree about the definition of an antiideal: do we assume ¬(0∈A)\neg(0\in A) or ∀p∈A,p#0\forall p\in 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)\neg (0\in A) as the definition (since 00 is a constant and ⊥\bot 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?

    • The statement had been laying dormant here for about a dozen years, without a proof. I’ve finally put some meat on the bones.

      diff, v2, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have expanded the Idea-section at deformation quantization a little, and moved parts of the previous material there to the Properties-section.

    • entry renamed to fit more systematic naming pattern

      diff, v29, current

    • replaced broken link to Witten’s paper with doi

      diff, v3, current

    • Recorded definition and basic properties.

      v1, current

    • 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\lambda Ring of λ\lambda-rings is monadic and comonadic over the category of CRingC Ring of commutative rings.

      b) The category λRing ¬tor\lambda Ring_{\neg tor} of λ\lambda-rings is monadic and comonadic over the category of CRing ¬torC Ring_{\neg tor} of commutative rings.

      diff, v46, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • a stub, for the moment just so as to satisfy links and record references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • 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.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • 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

      • Ieke Moerdijk, Cyclic sets as a classifying topos, 1996 (pdf)

      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.

    • It seemed helpful to have a separate page to discuss the precise relationship between coherence and strictification, that could be linked to from both pages.

      v1, current

    • 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.

      v1, current

    • Page created, but author did not leave any comments.

      Jade Master

      v1, current

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