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    • I added some simpler motivation in terms of the basic example to the beginning of distributive law.

    • started a still highly stubby entry on nonabelian Hodge theory.

      So far all I have is some references and the statement of "Corlette's theorem".

    • created Hodge structure. Currently with nothing but a pointer to this nice book:

      • Chris Peters, Jozef Steenbrink, Mixed Hodge Structures, Ergebisse der Mathematik (2007) (pdf)

      Eventually I’d think we should move over Hodge-structure articles from Hodge theory to here. But not tonight.

    • The notion interpolating between Higgs bundles/sheaves and bundles/sheaves with flat connections.

      v1, current

    • Right, have changed that. Also two instances of multiple letters in a \mathcal{} weren’t compiling, so I’ve removed them.

      diff, v7, current

    • Mauro Spera is an Italian mathematical physicist.

      v1, current

    • added rules for function types as types of anafunctions

      Anonymous

      diff, v15, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • the concept of a weak type theory as a dependent type theory where all type formers are weak in the sense that they use identity types instead of judgmental equality in the computation and uniqueness rules

      Anonymouse

      v1, current

    • now creating this entry.

      The technical material under “Details” (here) is copied over from what I had written at reader monad – Examples – quantum reader monad. (There may still be room left to adjust the wording in order to reflect that this material moved to a new entry.)

      To this I have now added an Idea-section (here) which highlights the relation to (equivalence with) Bob Coecke’s “classical structures” (which term I made redirect to here now)

      v1, current

    • Starting an entry (to rhyme on “quantum reader monad”) on the linear version of the costate comonad and how its coKleisli category on the tensor unit alone exhibits the structure of quantum observables.

      v1, current

    • Am starting a write-up (here) of how (programming languages for) quantum circuits “with classical control and/by measurement” have a rather natural and elegant formulation within the linear homotopy type theory of Riley 2022.

      Aspects of this have a resemblance to some constructions considered in/with “Quipper”, but maybe it helps clarify some issues there, such as that of “dynamic lifting”.

      The entry is currently written without TOC and without Idea-section etc, but rather as a single top-level section that could be !include-ed into relevant entries (such as at quantum circuit and at dependent linear type theory). But for the moment I haven’t included it anywhere yet, and maybe I’ll eventually change my mind about it.

      v1, current

    • recording some reference in reply to the question: “What about quantum channels that admit an environmental representation where the environment starts out in its maximally mixed state?”

      v1, current

    • Minimal person entry on a Slovenian mathematician, his formula plays major role in the entry principal value.

      v1, current

    • I want to be adding some details to Cauchy principal value. What’s a good reference? Say for the proof that up to addition of a delta-distribution, f(x)=pv(1x)f(x) = pv\left( \frac{1}{x}\right) is the unique distributional solution to xf=1x f = 1?

    • a small entry, for ease of direct hyperlinking of the concept

      v1, current

    • starting some minimum, for completeness

      v1, current

    • this kind of page has been missing,

      starting something with (currently just) the least general (but maybe most important) version of the definition (MacLane’s “conjugate” transformations) with a brief comment on the relation to bifibrations.

      v1, current

    • started page to make links work

      Anonymouse

      v1, current

    • starting article on the PostBQP complexity class

      Anonymouse

      v1, current

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

    • starting article on semisimple rings

      Anonymous

      v1, current

    • added pointer to:

      • Rob Norris, Functional Programming with Effects, talk at Scala Days 2018 [video: YT]

      diff, v56, current

    • a stub entry, for the moment just to make links work

      v1, current

    • I haven’t seen anyone admit to a precise operational definition of QRAM, but it seems clear that it must be that which is seen by the “linear state monad” LinMaps(QMem,QMem⊗A)LinMaps\big( QMem , QMem \otimes A\big). Besides recording the two original references, this is what the entry now briefly says.

      v1, current

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

      v1, current

    • a bare list of references, to be !include-ed into the references lists of relevant entries

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Added a literature reference to icon. Started some systematic notes on icons for monoidal-enriched bicategories, which I am currently using for something. Think the broken-off state of that section is not intolerable, in particular since I have seen similar work in progress on the nLab. Intend to continue them soon.

    • I added a section on strictification of pseudofunctors C→CatC \to Cat to pseudofunctor, after seeing Finn and Mike respond to Karol in the stable monoidal derivator thread at the Café. The discussion is fairly sketchy and pedestrian. Also added a few references.

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Wikipedia has a nice article on quantum operations.

      The nLab also had a page quantum operations and channels (cache bug?), but I’ve renamed this to simply quantum operation since a quantum channel seems to be nothing but a quantum operation when viewed from the perspective of quantum information theory. Eventually, this page might need some disambiguation since there may be several uses of the term, but for now I think it is “ok”.

      I think this page can be cleaned up. I started, but don’t think I will be able to finish.

      In particular, there is some background material that might be better on separate pages. I’ll continue trying to clean things up, but family might be calling soon and I’ll need to run quickly whatever state it is in.

      I also made the simple statement

      In quantum mechanics, a quantum operation is a morphism in the category of density matrices

      at the beginning of the Idea section motivated by O’Loan’s comment

      A quantum channel is a mapping which sends density matrices to density matrices.

      This seems innocent enough, but someone might check the statement. For one, I’ve never seen a category of density matrices, but the idea seems obvious enough. Maybe a word on density matrix would be good.

    • this is a bare sub-section — meant to be !includeed into relevant entries such as at quantum channel and at quantum decoherence — towards the theorem that quantum channels are exactly the “bath-averages of bath-coupled unitary evolutions”

      v1, current

    • recorded some recent surveys of the status of MOND at MOND

    • a bare minimum, for the moment just to make links work

      v1, current

    • Added the characterization of CompComp as the unique non-trivial pretopos which is well-pointed, filtral and admits all set-indexed copowers of its terminal object from

      • Vincenzo Marra, Luca Reggio, A characterisation of the category of compact Hausdorff spaces, (arXiv:1808.09738)

      diff, v25, current

    • Basic start for the notion introduced by Dyckerhoff and Kapranov.

      v1, current

    • starting a bare minimum, to make links work.

      (The single example included is copied over from revision 1 of partial trace, where I had deleted it as announced there. It needs attention, if only for the typesetting).

      v1, current

    • Just added a page on partial trace that is presently linked from quantum operations and channels which I also added to. However, note that the partial trace is not specific to physics so it needs embellishing by the mathematicians among us.

    • brief category:people-entry for hyperlinking references

      v1, current

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