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nLab > Latest Changes: commutativity of homotopy limits and colimits

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 14th 2023

    Created:

    Idea

    …

    Definition

    …

    Related concepts

    References

    • Section A.5, in particular, Definition A.5.2.1, Theorems A.5.3.1, A.5.4.1, A.5.6.1 in Lurie’s Spectral Algebraic Geometry.

    Earlier lecture notes by Lurie: https://www.math.ias.edu/~lurie/287xnotes/Lecture7.pdf.

    For a treatment without ∞-categories, see also Definition 3.2 in arXiv:1912.10544.

    Rezk’s manuscript discusses how to commute base changes past realizations:

    An even larger class of maps of so-called weak Kan fibrations is studied in Section 3 of

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2023
    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 14th 2023

    Massively expanded the description. Added references.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2023

    I have grouped the references on pullback-stability of realization together, added pointer to the original article by Bousfield & Friedlander, brought them into chronological order and added pointer to where on the nLab this is discussed (see above).

    Replaced the duplicate reference to Pavlov et al. by a cross-link (but it remains unclear: you are pointing to Def. 3.2 in there but not to a statement on commutativity of homotopy limits with colimits, as one would expect).

    Hyperlinked the mentioning of model (∞,1)-categories, added the missing data to references by Mazel-Gee.

    But these pointers and also those to Cisinski’s and Lurie’s books remain too unspecific to be useful for this entry: You should say which statements in these general-purpose monographs you mean to point out in the context of this entry.

    Also added table of contents and context menu, as usual.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 16th 2023

    Refined the references.

    diff, v4, current

1 to 5 of 5

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