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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 12th 2014
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   Author: Dmitri Pavlov
   Format: MarkdownItexHomotopy 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?

   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?

2. • CommentRowNumber2.
   • CommentAuthorZhen Lin
   • CommentTimeDec 12th 2014
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   Author: Zhen Lin
   Format: MarkdownItexThe category $\mathbf{\Delta}^{op}$ has an initial object, so its homotopy limit is natural equivalent to the value of the diagram at that vertex.

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

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 12th 2014
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   Author: Dmitri Pavlov
   Format: MarkdownItexIndeed, I forgot to take the opposite category when I considered this possibility.

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