the link to the picture in the entry *Charles Wells* is broken. Does anyone know how to fix it or have an alternative picture?

starting something. There is nothing to be seen yet, but I need to save.

]]>Created a page of that sort of Grothendieck topology.

]]>have recovered the pdf file and upload to the nLab server (now here: pdf)

]]>added a couple of references, touched others

]]>Added this pointer:

An early discussion of automata via string diagrams in the Cartesian monoidal category of finite sets:

- Günter Hotz,
Eine Algebraisierung des Syntheseproblems von Schaltkreisen, EIK, Bd. 1, (185-205), Bd, 2, (209-231) 1965 (part I, part II, compressed and merged pdf)

incuding that new compressed and merged pdf which I produced, as a service to the community.

]]>In looking for texts that would address the question “What is computation?” and arrive at an answer vaguely akin to path lifting/transport, I found (and have now added pointer to) this text:

- Jan van Leeuwen, Jiří Wiedermann:
*Knowledge, Representation and the Dynamics of Computation*, pp. 69-89 in:*Representation and Reality in Humans, Other Living Organisms and Intelligent Machines*, Studies in Applied Philosophy, Epistemology and Rational Ethics**28**, Springer (2017) [doi:10.1007/978-3-319-43784-2_5, pdf]

which gets pretty close, in particular in and around their Figure 1.

]]>I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to

]]>In locally cartesian closed category, I wrote out an explicit proof that pullback functors $f^\ast \colon C/Y \to C/X$ between slices preserve exponentials (so that Frobenius reciprocity is satisfied).

]]>I reorganized linearly distributive category by moving the long block of history down to the bottom, adding an “Idea” section and a description of how $*$-autonomous categories give rise to linearly distributive ones and linearly distributive ones give rise to polycategories. I also cross-linked the page better with polycategory and star-autonomous category.

]]>I added some examples of virtual double categories that do not have composites described in Crutwell-Shulman.

]]>A stub recording a reference:

In a double category $C$ with companions, a **retrocell** is …

In the double category of spans, a retrocell boils down to a morphism of spans, where the source span is the pullback of the original source span along the corresponding horizontal arrow. (Paré, §5.)

- Robert Paré,
*Retrocells*, arXiv:2306.06436.

Changes made only to the Universal property of the 2-category of spans section. The citations by Urs lead to another citation which, in turn, leads to another citation. With a little effort, I tracked down the a full copy of said universal property, I’ve replicated it here, added the citation used, although I left the previous citations there for convenience; a more experienced editor can remove those if they would like.

I would like to note that the author whose work I have referenced, Hermida, also notes: “[this universal property] is folklore although we know no references for it.”

Please make any corrections needed and clean up the language here; this is a fairly direct copy of what is written, but I imagine somebody with more knowledge of all the language used here can rewrite this universal property stuff in a cleaner way.

Thanks!

Anonymous

]]>Expanded dinatural transformation a little with examples and references.

]]>I’ve created this discussion following the recent posts in the discussion of fivebrane 6-group and since I have two more points that are unclear to me:

- What about capitalization? Fivebrane group is capitalized and fivebrane 6-group is uncapitalized. According to HowTo, “page titles should be uncapitalized, except for words that are always capitalized.” As far as I know, spin and string groups are always uncapitalized as text, while Fivebrane and Ninebrane groups are always capitalized as text. (With all of them capitalized in formulas of course.)
- What about hyphens? There are examples, where one seems to be missing, for example Fréchet Lie group and Conner-Floyd Chern class.
- What about superscripts? Unicode provides letters in superscript, which for example enables to create a page titled spinᶜ while the current page is titled spin^c. Another example is MSpin^c.

For now creating page, more to be added soon.

]]>added pointer to:

- Jiří Adámek, Horst Herrlich, George Strecker, Def. 7.71 in:
*Abstract and Concrete Categories – The Joy of Cats*John Wiley and Sons, New York (1990) reprinted as: Reprints in Theory and Applications of Categories**17**(2006) 1-507 (tac:tr17, book webpage, pdf)

created Frobenius monoidal functor

]]>Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor

Todo: add more proofs of this result.

For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:

An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out

How can I fix this?

]]>link to PDF for reference

]]>a stub, to satisfy links

]]>Created page.

]]>I added to initial object the theorem characterizing initial objects in terms of cones over the identity functor.

]]>brief `category:people`

-entry for hyperlinking references