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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 17th 2009
   • (edited Dec 17th 2009)
   • PermaLink
   Author: Urs
   Format: MarkdownWith Zoran I am working on entries related to monadic descent. While that is underway, I have added to * [[Sweedler coring]] a section * <a href="http://ncatlab.org/nlab/show/Sweedler+coring#GeomInterpretationOfCoring">geometric interpretation of the coring</a> and * <a href="http://ncatlab.org/nlab/show/Sweedler+coring#GeomInterpretationOfDescent">geometric interpretation of comodule descent</a>

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

   • Sweedler coring

   a section

   • geometric interpretation of the coring

   and

   • geometric interpretation of comodule descent
2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 5th 2011
   • (edited Aug 5th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexon the nCafé [here](http://golem.ph.utexas.edu/category/2011/02/structured_ring_spectra_2011.html#c039018) Jim Stasheff asks who the "Sweedler" in [[Sweedler coring]] is . I don't know. Zoran?

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

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeAug 5th 2011
   • (edited Aug 5th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexSweedler 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 [[zoranskoda:compatible idempotent monads]], [[zoranskoda:domain globalization of functors]] and [[zoranskoda:global Hopf-Galois extension]] which I am going to expand soon. One needs flatness of $G$ 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).

   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 $G$ 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).

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 5th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> 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!

   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!

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 6th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexJim has more questions on Sweedler [here](http://golem.ph.utexas.edu/category/2011/02/structured_ring_spectra_2011.html#c039038). Please, everyone who replies to Jim, please don't forget to enter whatever information you have also into the relevant $n$Lab entry. For instance into the entry _[[Moss Sweedler]]_

   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 $n$Lab entry. For instance into the entry Moss Sweedler

6. • CommentRowNumber6.
   • CommentAuthorzskoda
   • CommentTimeAug 8th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI 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.

   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.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeNov 17th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have cross-linked _[[Sweedler coring]]_ with _[[Adams spectral sequence]]_ a little. That canonical cosimplicial object induced from an $E_\infty$-algebra is its "Sweedler $\infty$-coring". For whatever that's worth-

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

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeNov 26th 2013
   • (edited Nov 26th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded the following (and thereby the first) reference to _[[Sweedler coring]]_ * [[Tomasz Brzezinski]], [[Robert Wisbauer]], _Corings and Comodules_, Cambridge University Press, London Math. Soc. LN 309 (2003), ([errata pdf](http://www.math.uni-duesseldorf.de/~wisbauer/corinerr.pdf)) In section 29 this has a good discussion of the [[Amitsur complex]] and the descent theorem. Added a pointer there, too.

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

   • Tomasz Brzezinski, Robert Wisbauer, Corings and Comodules, Cambridge University Press, London Math. Soc. LN 309 (2003), (errata pdf)

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