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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• giving this a little entry

• Created this entry

• Added the definition of a unital comonoid, with string diagrams

• removing old comment in query box

+– {: .query} Madeleine Birchfield: Wouldn’t an ordinal number be an object of the decategorification of the category of well-ordered sets, just as a natural number is an object of the decategorification of the category FinSet? =–

Anonymous

• Added the contents of the canonical isomorphism induced by some non-canonical isomorphism as coming from Lack’s proof.

• Created the entry

• Todd,

when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

Thanks!

• started entry on category of monoids. Spelled out the free monoid construction. Stated the construction of pushouts of monoids along free maps with reference to Schwede-Shipley. Will fill in the proof in a moment.

• I gave the (counter-)example of the epimorphic ring inclusion $\mathbb{Z} \hookrightarrow \mathbb{Q}$ a numbered environment and a line of proof (here)

• I have added to primitive element the definition of primitive elements in comodules, and their equivalent characterization in terms of cotensor products. Added also a corresponding remark to cotensor product.

• I started to greatly expand the entry module

The new toc now looks like this:

• Idea

• Basic idea

• More general perspectives

• Enriched presheaves

• Stabilized overcategories

• Details

• Ordinary concept

• In enriched category theory

• Examples

• Modules over rings
• Related concepts

• Vector bundles and sheaves of modules
• starting article on a degree of a polynomial, since its entry in the disambiguation page degree linked to a nonexistent page.

Anonymous

• am starting some minimum here. Have been trying to read up on this topic. This will likely become huge towards beginning of next year

• Added the definition of homogeneous polynomials and the Euler identity.

• Init page on synthetic guarded domain theory. Hope to fill this in more as I learn more about the field.

• Added the statement.

• 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.

• A few words and an hyperlink to a page where I will put my conjectural characterization of symmetric powers in symmetric monoidal categories enriched over modules over a $\mathbb{Q}^{+}$-algebra.

• Added to bimonoid the fact that the category of modules over a bimonoid is monoidal.

• Created page.

• Added definition.

• Added a reference. May edit more later.

• Added writings on p-adic Hodge theory.

• The page on inductive-inductive types refers to dialgebras without specifying them. Having a short page as some sort of reference is helpful.

• starting article on the notion of local field in commutative algebra, which is slightly different from the notion of local field in algebraic number theory.

Anonymous

• For now created page, and written definition. Work in progress! (No surgical cut-and-paste from other pages will be performed.)

• Started an article on monoidal monad. An earlier redirect had sent it over to Hopf monad which is something that Zoran was working on, but I think it deserves an article to itself, with discussion of the relation to commutative monads, etc. (which I have started).

• Explain the connection with enriched monads

• brief category:people-entry for hyperlinking references

• Am trying to get some historical citations straight at linear type theory, maybe somebody can help me:

what are the original sources of the idea that linear logic/type theory should generally be that of symmetric monoidal categories (“multiplicative intuitionistic LL”)?

In order of appearance, I am aware of

• de Paiva 89 gives one particular example of a non-star-autonomous SMC that deserves to be said to interpret “linear logic” and clearly identifies the general perspective.

• Bierman 95 discusses semantics in general SMCs more generally

• Barber 97 reviews this and explores a bit more.

What (other) articles would be central to cite for this idea/perspective?

I am aware of more recent reviews such as

but I am looking for the correct “original sources”.

• creating stub article

Anonymous

• brief category:people-entry for hyperlinking references

• entry renamed to fit more systematic naming pattern

• New reference entry FAC aka Faisceaux algébriques cohérents. And few improvements to coherent sheaf including historical note.

• starting a dedicated entry for the category of vector bundles with homomorphisms allowed to cover non-trivial base maps (while previously we only had VectBund(B) for fixed base $B$).

For the moment the main point is to record the interesting cartesian- and tensor-monoidal structure (now here)

• added pointer also to this recent review in a popular magazine, which is well-informed about the contested status of the “island conjecture”:

• Nirmalya Kajuri, Of Islands, Holograms and Saving Quantum Physics From a Black Hole Paradox, Science – The Wire (Nov 2022)

[…] a few sceptics have argued that while the calculations are correct, they don’t help resolve the black hole information-loss paradox. The troubles stem from the reservoir attached to the anti-de Sitter universe. The physicists who authored the island papers assumed that gravity stopped at the boundary of the anti-de Sitter space and didn’t enter the reservoir. This is not an innocuous assumption. […] The key takeaway is that the island way to recover information and save unitarity works perfectly well – if you slightly modify Einstein’s theory of gravity. These criticisms have been around for some two years now, and physicists are yet to resolve them in print. […] physicists continue to publish papers by the hundreds about the entanglement islands but few attempt to answer whether the islands are compatible with the Einsteinian gravity of our universe. […]

I think i will create an include-file now for these references, so that it will be easier to sync with other entrties, such as Bekenstein-Hawking entropy:

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• Added an article

• for completeness

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• a bare sub-section with a list of references – to be !included into relevant entries – mainly at confinement and at mass gap problem (where this list already used to live)

• in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity

• brief category:people-entry for hyperlinking references

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