thought we need such an entry; started something, so far with cross-links to *Riemann hypothesis*, *volume conjecture* and *image of beta*

Copied some of Mike’s blog post to indexed monoidal category, having worked on Charles Peirce if you want to know why. It needs wikifying.

]]>At the old entry *cohomotopy* used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.

(We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

]]>I have turned *logos* from a redirect to *Heyting category* into a stand-alone disambiguation entry, to account for Joyal’s proposal from 2008 (maybe meanwhile abandoned?) to say “logos” for “quasi-category”.

added PhD information

linked to her Academia page, which I believe she uses as her website

“category: people”

Joe M

]]>I just added a few basic links. I’ll add links to papers where monoidal versions of indexed categories and fibrations have shown up.

Joe M

]]>added to [[Grothendieck construction]] a section Adjoints to the Grothendieck construction

There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.

There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.

]]>edited dualizable object a little, added a brief paragraph on dualizable objects in symmetric monoidal $(\infty,n)$-categories

]]>I added the reference

- Nima Rasekh,
*A Theory of Elementary Higher Toposes*, (arXiv:1805.03805)

The cut rule for linear logic used to be stated as

If $\Gamma \vdash A$ and $A \vdash \Delta$, then $\Gamma \vdash \Delta$.

I don’t think this is general enough, so I corrected it to

]]>If $\Gamma \vdash A, \Phi$ and $\Psi,A \vdash \Delta$, then $\Psi,\Gamma \vdash \Delta,\Phi$.

Pi Calculus

Ammar Husain

]]>stub for homotopy type theory

]]>Strangely, we don’t seem to have an nForum discussion for probability theory.

I added a reference there to

- Chris Heunen, Ohad Kammar, Sam Staton, Hongseok Yang,
*A Convenient Category for Higher-Order Probability Theory*, (arXiv:1701.02547)

It replaces the category of measurable spaces, which isn’t cartesian closed, with the category of quasi-Borel spaces, which is. As they point out in section IX, what they’re doing is working with concrete sheaves on an established category of spaces, rather like the move to diffeological spaces.

[Given the interest in topology around these parts at the moment, we hear of ’C-spaces’ as generalized topological spaces arising from a similar sheaf construction in C. Xu and M. Escardo, “A constructive model of uniform continuity,” in Proc. TLCA, 2013.]

]]>I have created an entry on the *quaternionic Hopf fibration* and then I have tried to spell out the argument, suggested to me by Charles Rezk on MO, that in $G$-equivariant stable homotopy theory it represents a non-torsion element in

for $G$ a finite and non-cyclic subgroup of $SO(3)$, and $SO(3)$ acting on the quaternionic Hopf fibration via automorphisms of the quaternions.

I have tried to make a rigorous and self-contained argument here by appeal to Greenlees-May decomposition and to tom Dieck splitting. But check.

]]>Even stubbier.

]]>A stub.

]]>time to give this a table-for-inclusion, for cross-linking relevant entries

]]>am changing page name from “…F-theory…” to “…M/F-theory” since I will now add discussion and references in that more general case

]]>created an entry *[[modal type theory]]*; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with *[[monad (in computer science)]]*.

Link to S5 and S4(m)

Ammar Husain

]]>am finally splitting this off from *Hopf degree theorem*, to make the material easier to navigate. Still much room to improve this entry further (add an actual Idea-statement to the Idea-section, add more examples, etc.)

added list of references

]]>changed title to match more systematic naming convention

]]>stub for *dark matter*

I moved [[(n,k)-transformation]] to [[transfor]], as seemed to be agreed upon by those who spoke up in the discussion there.

]]>