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nLab > Latest Changes: t-structure

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2013

    added the definition to the old stub t-structure. Also redicrecting heart, of course. And also for stable ∞-categories.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 19th 2013

    Added some into references.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeNov 19th 2013

    I also added links to the papers of M. Douglas to the related entry Bridgeland stability.

    • CommentRowNumber4.
    • CommentAuthorFosco
    • CommentTimeNov 1st 2014

  5. I added to t-structure the condition that the two subcategories which comprise a t-structure have to be strictly full subcategories. I believe that this is the standard convention (see Gelfand/Manin, Goerss/Jardine, …).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023
    • (edited Apr 7th 2023)

    have added publication data to this item:

    • Domenico Fiorenza, Fosco Loregian, t-structures are normal torsion theories, Appl Categor Struct 24 (2016) 181–208 [arxiv:1408.7003, doi:10.1007/s10485-015-9393-z]

    and have replaced this item

    • Domenico Fiorenza and Fosco Loregian, “Hearts and Postnikov towers in stable ∞-categories” (in preparation)

    with what I suppose is the result of this preparation:

    Beware that the entry text refers to a “Theorem 2.16” in the article-in-preparation. I haven’t yet hunted for what number this corresponds to in the actual article.

    diff, v9, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    looks like the reference for that proposition should be Theorem 6.3 in FLM19

    diff, v11, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    added (here) mentioning of the archetypical example of the canonical t-structure on a derived category

    diff, v11, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    the wording in the second paragraph of “In stable ∞-categories” (here) was quite mangled. I have tried to adjust, but there may be room left to further expand on this.

    diff, v11, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    added pointer to:

    diff, v12, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    added (here) brief mentioning of the example of the canonical t-structure on spectra (deserves to be expanded further…)

    diff, v13, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeApr 7th 2023

    have made explicit (here) the definition of t-structures on stable ∞-categories

    and have moved the previous discussion relating to “normal torsion theories” out of the “Definition”-section into a dediated subsection under “Properties” (now here)

    diff, v14, current

1 to 12 of 12

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