# Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions

@article{Riehl2014CompletenessRF, title={Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions}, author={Emily Riehl and Dominic R. Verity}, journal={arXiv: Category Theory}, year={2014} }

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting these (co)limits and that they are preserved by the functors in the limit cone. In particular, the Bousfield-Kan homotopy limit of a diagram of quasi-categories admit any limits or colimits existing in and preserved by the functors in that diagram. In… Expand

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