added publication data to:

- Pedram Hekmati, Michael Murray, Richard Szabo, Raymond Vozzo,
*Sign choices for orientifolds*, Commun. Math. Phys. 378, 1843–1873 (2020) (arXiv:1905.06041)

added pointer to today’s

- Christian S. Fischer, Paul C. Wallbott, Richard Williams, Nico Santowsky, Gernot Eichmann,
*The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach*(arXiv:2007.06495)

Added result discussed at the Cafe that tensor products of symmetric pseudomonoids are a weak 2-coproduct.

]]>Added the result discussed at the Cafe that the cartesian product of symmetric monoidal categories is their (weak) 2-biproduct.

]]>Small changes.

]]>added pointer to today’s

- George Manolakos, Gregory Patellis, George Zoupanos,
*$\mathcal{N}=1$ trinification from dimensional reduction of $N=1$, 10D $E_8$ over $SU(3)/U(1)\times U(1) \times \mathbb{Z}_3$ and its phenomenological consequences*(arXiv:2009.07059)

Not that that article in #34 is explicitly about dependent types, but this page is a redirect for ’comprehension category’, and is the only place as yet to add it.

At some point it would be good to get back to whatever it is that connects Paul-André et al.’s work on refinement (glimpsed at times in the article) with Mike et al.’s work on modality.

]]>Added a new graphics (here), from today’s GMV 20 (Fig. 9 there)

]]>added pointer to today’s

- Valerio Gherardi, David Marzocca, Elena Venturini,
*Low-energy phenomenology of scalar leptoquarks at one-loop accuracy*(arXiv:2008.09548)

added pointer to today’s

- N. Penalva, E. Hernández, J. Nieves,
*$\bar B_c \to \eta_c$, $\bar B_c \to J/\psi$ and $\bar B \to D^{(\ast)}$ semileptonic decays including new physics*(arXiv:2007.12590)

Is there a way to copy the mathematical symbols in titles such as these and paste them *in their LaTex source form*? Currently I am tediously re-coding all these titles when recording them on the nLab.

I see that clicking on the MathJax and navigating through the resulting menus eventually displays LaTeX code for each formula separately. But for copying the whole title that’s just barely more convenient the recoding it from scratch. I would like to just highlight the whole title, hit a key combination for “copy” and another for “paste” and have the proper source code be dropped into the nLab edit window at once. Is this possible?

]]>added pointer to today’s

- G. Ramalho,
*A covariant model for the decuplet to octet Dalitz decays*(arXiv:2002.07280)

added pointer to today’s

- Tanmoy Paul,
*Antisymmetric tensor fields in modified gravity: a summary*(arXiv:2009.07732)

Added a reference for comprehension categories

- Paul-André Melliès, Nicolas Rolland,
*Comprehension and quotient structures in the language of 2-categories*, (arXiv:2005.10015)

]]>Our main purpose and achievement in this paper is to exhibit the 2-categorical structures secretly at work in the 1-categorical approach to comprehension structures traditionally found in categorical logic.

Thanks for highlighting. Sure, I have changed to “inverse base geometric morphism” (in the pdf file here), to match the terminology actually introduced in 2.43. (Hm, and maybe ordering of these Propositions should be changed. But I left that as is for the moment.)

]]>Now done.

]]>Feel free to edit the page, it could do with some re-structuring and additions; I was writing quickly earlier just to try to improve things a little. I will adjust the offending paragraph now.

]]>It’s not true in general that a strict 2-functor between strict 2-categories is a biequivalence (i.e. is biessentially surjective on objects and an equivalence on hom-categories) iff it is part of an “equivalence of 2-categories” as currently defined on this page: the ’inverse’ of the 2-functor might only be a pseudofunctor, not a strict 2-functor. See Example 3.1 in Steve Lack’s paper *A Quillen model structure for 2-categories*.

There is something weird about how Proposition 2.34 in Proper Orbifold Cohomology is formulated. It talks about the “terminal inverse image functor”.

But inverse image functors go in the opposite direction from geometric morphisms. In particular, the terminal ∞-topos in the category of toposes and geometric morphisms because the initial ∞-topos in the category of toposes and inverse image morphisms. Equivalently, inverse image functors T→H, where H is a fixed ∞-topos and T is an arbitrary ∞-topos, form a slice ∞-category over H, and ∞Grpd→H is the initial object in this ∞-category.

]]>Rewrite Chris Brown's answer to Mike's question as an actual example.

]]>Tweaked things slightly to emphasise that the notion of biequivalence is relevant both when one is working with weak 2-functors and when one is working with strict ones.

]]>Correcting the terminology for the equivalences: ’strict equivalences’ was used before, which has a different meaning. What was intended, I think, was simply to refer to the fact that the functors are strict.

]]>Re #7: The description on the nlab page to which you link of the weak equivalences in Lack’s model structure on 2-Cat as the “strict equivalences” is incorrect

I think that what was intended on that page was to refer to the fact that the functors are strict. I’ll correct it.

]]>I have fixed it now. The problem came from the table of contents rendering; the problem was the use of a customised theorem name in the theorems attributed to Hopkins-Singer and Bunke-Schick, which caused the renderer to think that these theorems were sections. Unnumbered theorem environments were also being used. I have now changed the environments to numbered ones, and added the attributions to Hopkins-Singer and Bunke-Schick in a slightly different way which does not break things.

]]>I have added references, but upon saving and now upon viewing the entry, it throws the following error message:

```
XML Parsing Error: mismatched tag. Expected: </div>.
Location: https://ncatlab.org/nlab/show/differential+cohomology
Line Number 545, Column 3:
</ul>
--^
```

Apparently this is caused by some code that was there before, which got re-saved now with a stricter parser. But I haven’t found the problematic line yet…

]]>