brief `category:people`

-entry for hyperlinking references

I have begun cleaning up the entry cycle category, tightening up definitions and proofs. This should render some of the past discussion obsolete, by re-expressing the intended homotopical intuitions (in terms of degree one maps on the circle) more precisely, in terms of “spiraling” adjoints on the poset $\mathbb{Z}$.

Here is some of the past discussion I’m now exporting to the nForum:

]]>The cycle category may be defined as the subcategory of Cat whose objects are the categories $[n]_\Lambda$ which are freely generated by the graph $0\to 1\to 2\to\ldots\to n\to 0$, and whose morphisms $\Lambda([m],[n])\subset\mathrm{Cat}([m],[n])$ are precisely the functors of degree $1$ (seen either at the level of nerves or via the embedding $\mathrm{Ob}[n]_\Lambda\to \mathbf{R}/\mathbf{Z}\cong S^1$ given by $k\mapsto k/(n+1)\,\mathrm{mod}\,\mathbf{Z}$ on the level of objects, the rest being obvious).

The simplex category $\Delta$ can be identified with a subcategory of $\Lambda$, having the same objects but with fewer morphisms. This identification does not respect the inclusions into $Cat$, however, since $[n]$ and $[n]_\Lambda$ are different categories.

started *cubical type theory* using a comment by Jonathan Sterling

category: people page for Johannes Schipp von Branitz

Anon

]]>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.

Create page, add some initial references. Referenced from the ’category theory’ page.

]]>starting page on impredicative polymorphism in dependent type theory

Anonymouse

]]>starting discussion page for this page

Anonymous

]]>Inspired by a discussion with Martin Escardo, I created taboo.

]]>Created polymorphism.

]]>A stub.

]]>Add references relating to rewriting.

]]>starting disambiguation page on impredicative universes

Anonymouse

]]>I added this to the entry for Nima Arkani-Hamed.

Urs (or anyone else) do you know anything about Nima’s recent interest in category theory?

“six months ago, if you said the word category theory to me, I would have laughed in your face and said useless formal nonsense, and yet it’s somehow turned into something very important in my intellectual life in the last six months or so” (@ 44:05 in The End of Space-Time July 2022)

]]>Cite Virtual Equipment Type Theory.

]]>A combinatorial notion in the study of total positivity.

]]>for completeness, to go with the other entries in *coset space structure on n-spheres – table*

replaced broken link to Witten’s paper with doi

]]>Added work on Ologs and started restructuring the page

rTuyeras

]]>This is for olog-specific stuff which wouldn’t be appropriate for biology.

]]>I looked at *real number* and thought I could maybe try to improve the way the Idea section flows. Now it reads as follows:

]]>A

real numberis something that may be approximated by rational numbers. Equipped with the operations of addition and multiplication induced from the rational numbers, real numbers form anumber field, denoted $\mathbb{R}$. The underlying set is thecompletionof the ordered field $\mathbb{Q}$ of rational numbers: the result of adjoining to $\mathbb{Q}$ suprema for every bounded subset with respect to the natural ordering of rational numbers.The set of real numbers also carries naturally the structure of a topological space and as such $\mathbb{R}$ is called the

real linealso known asthe continuum. Equipped with both the topology and the field structure, $\mathbb{R}$ is a topological field and as such is the uniform completion of $\mathbb{Q}$ equipped with the absolute value metric.Together with its cartesian products – the Cartesian spaces $\mathbb{R}^n$ for natural numbers $n \in \mathbb{N}$ – the real line $\mathbb{R}$ is a standard formalization of the idea of

continuous space. The more general concept of (smooth)manifoldis modeled on these Cartesian spaces. These, in turnm are standard models for the notion of space in particular in physics (seespacetime), or at least in classical physics. See atgeometry of physicsfor more on this.

added publication data for these two items:

Rui Loja Fernandes, Marius Crainic,

*Integrability of Lie brackets*, Ann. of Math.**157**2 (2003) 575-620 [arXiv:math.DG/0105033, doi:10.4007/annals.2003.157.575]Rui Loja Fernandes, Marius Crainic,

*Lectures on Integrability of Lie Brackets*, Geometry & Topology Monographs**17**(2011) 1–107 [arxiv:math.DG/0611259, doi:10.2140/gtm.2011.17.1]

have added a minimum on the level decompositon of the first fundamental rep of $E_{11}$ here.

]]>I have half-heartedly started adding something to *Kac-Moody algebra*. Mostly refrences so far. But I don’t have the time right now to do any more.

have created enriched bicategory in order to help Alex find the appropriate page for his notes.

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