Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • Added the definition of a unital comonoid, with string diagrams

      diff, v8, current

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

      diff, v32, current

    • 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)

      diff, v8, current

    • 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

      v1, current

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

      v1, current

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

      diff, v2, current

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

      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

    • 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.

      diff, v15, current

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

    • 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

      v1, current

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

      v1, current

    • 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).

    • brief category:people-entry for hyperlinking references

      v1, current

    • 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

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • entry renamed to fit more systematic naming pattern

      diff, v29, current

    • 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 BB).

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

      v1, current

    • 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:

      diff, v8, current

    • 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

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • 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)

      v1, current

    • 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

      v1, current

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

      v1, current