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nLab > Latest Changes: homotopy colimit

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2009

    Wrote a section General weighted colimit formula at homotopy colimit

    • giving a general formula

    • spelling out the special case of simplicial diagrams, that reproduces the Bousfield-Kan formula

    • spelling out the special case of pushout diagrams, that reproduces the formula (or its dual) discussed more in detail in the other examples that were already present

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2009
    • (edited Dec 14th 2009)

    started also a section on Homotopy (co)limits of simplicial (pre)sheaves at homotopy limit that states a nice result by Charles Rezk, that simplicial prolongations of inverse image functors are indeed homotopy left exact (well, he shows at least that they preserve homotopy pullbacks).

    This in particulal yields the model category version of the statement that oo-stackification is homotopy left exact (or, well, at least that it preserbes homotopy pullbacks).

  3. added a few lines in homotopy limit concerning the quotient and the homotopy quotient of a topological space by a group action, soon after EG and BG are mentioned in the examples.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 16th 2009
    • (edited Dec 16th 2009)

    Thanks!

    By the way, did I identify your website correctly, here?

  5. Yes, that's me! Thanks!

    By the way, is that the place where I should post current interests and work in progress or should I ask for a red page for that?
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 16th 2009
    • (edited Dec 16th 2009)

    It makes sense, in any case, to supply at the nLab page that carries your name some general information about who you are.

    On top of that, if you want, you can ask the steering committee to create a "personal web" for you, of the kind listed here. (Simply post a request in the category "General" here at the forum.)

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 16th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote> Yes, <a href="http://ncatlab.org/nlab/show/domenico_fiorenza">that's me</a>! </blockquote> <p>Okay, cool. I should tap your knowledge of L-oo and BV stuff at some point to jointly improve our pages on these matters.</p> </div>
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2011
    • (edited Jun 7th 2011)

    I have created at homotopy limit a new section “Computational methods” below the Definition-section. I gave it three subsections

    1. By ordinary (co)limits over resolved diagrams

    2. By resolved (co)ends

    3. By bar constructions

    and then moved some of the discussion that was previously in the Definition-section into the first two of these. I have not yet filled anything into the bar-construction section.

    But in the Examples-section I have expanded the section on hocolims of diagrams of spaces by adding a section on how to compute these using geometric realization of simplicial topological spaces, which is secretly an example of the bar-construction method. But I haven’t added discussion of the background yet.

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeJul 6th 2013

    [I hid a spam post with a URL for knock-off watches.]

    • CommentRowNumber10.
    • CommentAuthorAndrew Stacey
    • CommentTimeJul 10th 2013

    [So did I, and the other pointless comments - with anonymous comments then I’m going to be fairly ruthless: if it has no content, it shouldn’t be here and there’s no “benefit of the doubt”.]

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