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nLab > Latest Changes: dg-category

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  1.  
    • CommentRowNumber1.
    • CommentAuthoradeelkh
    • CommentTimeJan 7th 2015
    • (edited Jan 7th 2015)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 7th 2015

    Thanks! Maybe it’s time for a new floating table of contents “dg-Categories”.

    • CommentRowNumber3.
    • CommentAuthoradeelkh
    • CommentTimeJan 25th 2015

    I did some reorganization of the references, cleaned up some of the old query boxes, and rewrote some of the introduction at dg-category.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 9th 2015

    I fixed a dead link for Toen’s lecture notes. I think the earliest use of the notion is in Kelly’s paper from 1965. The terminology though is from much later and the development for applications other than homology theory as well.

    • CommentRowNumber5.
    • CommentAuthoradeelkh
    • CommentTimeFeb 9th 2015

    Thanks. I wonder if the idea of weak enrichment, i.e. enrichment up to quasi-isomorphism, is already present in that paper?

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 9th 2015
    • (edited Feb 9th 2015)

    My reference to Kelly is from Keller and means enriched in (Ch(A),⊗)(Ch(A),\otimes) or one of the bounded or semi-bounded variants. Weak enrichment is much later, I think. I don’t know if Jim Stasheff looks at that anywhere at that time.

    Some of Ross Street’s early papers were more in this chain complex setting than his later work would lead one to expect.

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 10th 2015

    Adeel, Is there (in the nLab or elsewhere) a good set of notes that explains the use of dg-categories in representation theory. I keep on seeing phrases that say how important an application it is but so far have not found a good introduction!

    • CommentRowNumber8.
    • CommentAuthoradeelkh
    • CommentTimeFeb 10th 2015

    I’m only aware of Keller’s survey, which if I recall correctly has some discussion of applications to representation theory. I’ll ask my friend Pieter Belmans if he has any recommendations.

    • CommentRowNumber9.
    • CommentAuthoradeelkh
    • CommentTimeFeb 10th 2015
    • (edited Feb 10th 2015)

    Pieter recommended Keller’s survey as well, specifically section 4.9 on orbit categories. He also mentioned that another interesting application is in this paper.

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 10th 2015

    Thanks (and thanks to Pieter). I will take a look.

    • CommentRowNumber11.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 16th 2018

    What happened to dg-category? The current page has removed all content from rev 41. Did we rename it?

    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 17th 2018

    Ah, from the last diff page, Zoran added a reference and changed a subtitle. Why isn’t the entry showing?

  13. Made it render now. Problem was that the page tried to include ’homological algebra - contents’, which apparently does not exist. Later I can check if there is some other variant of this contents page which was intended.

    • CommentRowNumber14.
    • CommentAuthorRichard Williamson
    • CommentTimeAug 17th 2018
    • (edited Aug 17th 2018)

    The page homological algebra - contents does exist, I have now added it back to dg-category (there must have been a typo or something before), and fixed a link.

    • CommentRowNumber15.
    • CommentAuthorTim_Porter
    • CommentTimeApr 19th 2023

    Fixed link to Tabuada’s thesis.

    diff, v47, current

    • CommentRowNumber16.
    • CommentAuthorperezl.alonso
    • CommentTimeMay 14th 2024
    • (edited May 14th 2024)

    pointer

    • Yuki Imamura. A formal categorical approach to the homotopy theory of dg categories (2024). (arXiv:2405.07873).

    diff, v48, current

1 to 16 of 16

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