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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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-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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2009
    • (edited Dec 17th 2009)

    With Zoran I am working on entries related to monadic descent. While that is underway, I have added to

    a section

    and

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 5th 2011
    • (edited Aug 5th 2011)

    on the nCafé here Jim Stasheff asks who the “Sweedler” in Sweedler coring is . I don’t know. Zoran?

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeAug 5th 2011
    • (edited Aug 5th 2011)

    Sweedler is a major author on Hopf algebras, authoring an old book in the subject, and a professor emeritus at Cornell. His work on noncommuytative extensions dealing with Sweedler coring and related work of his colleague from Cornell Chase on noncommutative Galois, predating Hopf-Galois theory is from 1970s.

    It is a pity that while one can make the descent for modules for noncommutative extensions, the descent for algebras (hence for affine schemes, as in SGA) works only in commutative case.

    While you are working on monadic and comonadic descent you may be interested in related recent pages compatible idempotent monads (zoranskoda), domain globalization of functors (zoranskoda) and global Hopf-Galois extension (zoranskoda) which I am going to expand soon. One needs flatness of GG in the page on global Hopf-Gaois extension (this page was a sketch before the meeting with Gabi where the things were cleared and which is not reflected in writing yet).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 5th 2011

    Sweedler is a major author on Hopf algebras, authoring an old book in the subject, and a professor emeritus at Cornell. His work on noncommuytative extensions dealing with Sweedler coring and related work of his colleague from Cornell Chase on noncommutative Galois, predating Hopf-Galois theory is from 1970s.

    Okay, thanks. I have copied that into the References-section at Sweedler coring

    While you are working on monadic and comonadic descent you may be interested in related recent pages

    I am not working on these entries at the moment. But if you link to your new entries from where it is relevant, then I will find them once I do!

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2011

    Jim has more questions on Sweedler here.

    Please, everyone who replies to Jim, please don’t forget to enter whatever information you have also into the relevant nnLab entry. For instance into the entry Moss Sweedler

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeAug 8th 2011

    I answered his question at cafe now though I see no importance in collecting the data for a person’s entry, while more central entries can not get our attention and time.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2013

    I have cross-linked Sweedler coring with Adams spectral sequence a little. That canonical cosimplicial object induced from an E E_\infty-algebra is its “Sweedler \infty-coring”. For whatever that’s worth-

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2013
    • (edited Nov 26th 2013)

    Added the following (and thereby the first) reference to Sweedler coring

    In section 29 this has a good discussion of the Amitsur complex and the descent theorem. Added a pointer there, too.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)