Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry 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 stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 1st 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the full definition to [[factorization algebra]]

   added the full definition to factorization algebra

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeDec 1st 2010
   • (edited Dec 1st 2010)
   • PermaLink
   Author: zskoda
   Format: MarkdownI added to [[factorization algebra]] today's reference from the arxiv: * Gregory Ginot, Thomas Tradler, Mahmoud Zeinalian, _Derived higher Hochschild homology, topological chiral homology and factorization algebras_, [arxiv/1011.6483](http://arxiv.org/abs/1011.6483) By the way, I find it useful that in the links for arxiv papers the number is seen/printed.

   I added to factorization algebra today's reference from the arxiv:

   • Gregory Ginot, Thomas Tradler, Mahmoud Zeinalian, Derived higher Hochschild homology, topological chiral homology and factorization algebras, arxiv/1011.6483

   By the way, I find it useful that in the links for arxiv papers the number is seen/printed.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMar 9th 2011
   • (edited Mar 9th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThis is quite interesting (slides, related subject): <http://www.ms.u-tokyo.ac.jp/~makoto/Tsukuba.pdf>

   This is quite interesting (slides, related subject):

   http://www.ms.u-tokyo.ac.jp/~makoto/Tsukuba.pdf

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 18th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have briefly added at [[factorization algebra]] a pointed to Gaitsgory-Francis.

   I have briefly added at factorization algebra a pointed to Gaitsgory-Francis.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 18th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso to [[chiral algebra]]

   also to chiral algebra

6. • CommentRowNumber6.
   • CommentAuthorjim_stasheff
   • CommentTimeJun 19th 2011
   • PermaLink
   Author: jim_stasheff
   Format: Texthttp://www.ms.u-tokyo.ac.jp/~makoto/Tsukuba.pdf that link doesn't work and I can't find that pdf on his home page

   http://www.ms.u-tokyo.ac.jp/~makoto/Tsukuba.pdf
   
   that link doesn't work
   and I can't find that pdf on his home page
7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeJun 19th 2011
   • (edited Jun 19th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexMaybe he changed the affiliation and lost the account. Google for te search Tsukuba Makoto site:www.ms.u-tokyo.ac.jp still gives the above URL as the first hit, so the change must have been very recent. The title of the document Tsukuba.pdf is "Recent developments of chiral categories". Makoto also has a blog <http://makotosakurai.blogspot.com> (maybe we should list it under [[math blogs]] ? but it seems to be inactive for a while) where at <http://makotosakurai.blogspot.com/2009/07/recent-developments-of-chiral.html> is an entry on this topic with the same obsolete pdf link as above.

   Maybe he changed the affiliation and lost the account. Google for te search

   Tsukuba Makoto site:www.ms.u-tokyo.ac.jp

   still gives the above URL as the first hit, so the change must have been very recent. The title of the document Tsukuba.pdf is “Recent developments of chiral categories”. Makoto also has a blog

   http://makotosakurai.blogspot.com (maybe we should list it under math blogs ? but it seems to be inactive for a while)

   where at http://makotosakurai.blogspot.com/2009/07/recent-developments-of-chiral.html is an entry on this topic with the same obsolete pdf link as above.

8. • CommentRowNumber8.
   • CommentAuthorzskoda
   • CommentTimeAug 30th 2016
   • PermaLink
   Author: zskoda
   Format: MarkdownItexA higher-dimensional generalization of vertex algebras is suggested in the framework of factorization algebras in * Emily Cliff, _Universal factorization spaces and algebras_, [arxiv/1608.08122](http://arxiv.org/abs/1608.08122) > We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a factorization algebra or space by an \'etale morphism of schemes, and hence to define the notion of a universal factorization space or algebra. This provides a generalization to higher dimensions and to non-linear settings of the notion of a vertex algebra.

   A higher-dimensional generalization of vertex algebras is suggested in the framework of factorization algebras in

   • Emily Cliff, Universal factorization spaces and algebras, arxiv/1608.08122

   We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a factorization algebra or space by an 'etale morphism of schemes, and hence to define the notion of a universal factorization space or algebra. This provides a generalization to higher dimensions and to non-linear settings of the notion of a vertex algebra.

9. • CommentRowNumber9.
   • CommentAuthorzskoda
   • CommentTimeMar 28th 2018
   • PermaLink
   Author: zskoda
   Format: MarkdownItexMore references listed at [[factorization algebra]].

   More references listed at factorization algebra.

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJul 6th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to today's * [[Araminta Amabel]], *Notes on Factorization Algebras and TQFTs* &lbrack;[arXiv:2307.01306](https://arxiv.org/abs/2307.01306)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/factorization+algebra/45">diff</a>, <a href="https://ncatlab.org/nlab/revision/factorization+algebra/45">v45</a>, <a href="https://ncatlab.org/nlab/show/factorization+algebra">current</a>

    added pointer to today’s

    • Araminta Amabel, Notes on Factorization Algebras and TQFTs [arXiv:2307.01306]

    diff, v45, current

11. • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeAug 2nd 2024
    • PermaLink
    Author: zskoda
    Format: MarkdownItexRelation with [[vertex algebras]] * Yusuke Nishinaka, _An algebraic construction of functors between vertex algebras and Costello--Gwilliam factorization algebras_, [arXiv:2408.00412](https://arxiv.org/abs/2408.00412) > We construct functors between the category of vertex algebras and that of Costello-Gwilliam factorization algebras on the complex plane ℂ, without analytic structures such as differentiable vector spaces, nuclear spaces, and bornological vector spaces. We prove that this pair of functors is an adjoint pair and that the functor from vertex algebras to factorization algebras is fully faithful. Also, we identify the class of factorization algebras that are categorically equivalent to vertex algebras. To illustrate, we check the compatibility with the commutative structures and the factorization algebras constructed as factorization envelopes, including the Kac-Moody factorization algebra, the quantum observables of the βγ system, and the Virasoro factorization algebra. <a href="https://ncatlab.org/nlab/revision/diff/factorization+algebra/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/factorization+algebra/49">v49</a>, <a href="https://ncatlab.org/nlab/show/factorization+algebra">current</a>

    Relation with vertex algebras

    • Yusuke Nishinaka, An algebraic construction of functors between vertex algebras and Costello–Gwilliam factorization algebras, arXiv:2408.00412

    We construct functors between the category of vertex algebras and that of Costello-Gwilliam factorization algebras on the complex plane ℂ, without analytic structures such as differentiable vector spaces, nuclear spaces, and bornological vector spaces. We prove that this pair of functors is an adjoint pair and that the functor from vertex algebras to factorization algebras is fully faithful. Also, we identify the class of factorization algebras that are categorically equivalent to vertex algebras. To illustrate, we check the compatibility with the commutative structures and the factorization algebras constructed as factorization envelopes, including the Kac-Moody factorization algebra, the quantum observables of the βγ system, and the Virasoro factorization algebra.

    diff, v49, current