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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 12th 2014

    Homotopy colimits of simplicial diagrams and homotopy limits of cosimplicial diagrams have their own special names: realization and totalization.

    Is there a special name for homotopy limits of simplicial diagrams? In general, are there any examples in the literature where such homotopy limits are computed?

    • CommentRowNumber2.
    • CommentAuthorZhen Lin
    • CommentTimeDec 12th 2014

    The category Δ op\mathbf{\Delta}^{op} has an initial object, so its homotopy limit is natural equivalent to the value of the diagram at that vertex.

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 12th 2014

    Indeed, I forgot to take the opposite category when I considered this possibility.