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Abstract
Consider a diagram of quasicategories 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 quasicategory admitting these (co)limits and that they are preserved by the functors in the limit cone. In particular, the BousfieldKan homotopy limit of a diagram of quasicategories admits any (co)limits existing in and preserved by the functors in that diagram. In previous work, we demonstrated that the quasicategory of algebras for a homotopy coherent monad could be described as a weighted limit of this type, so these results specialise to (co)completeness results for quasicategories of algebras. The second half of this paper establishes a further result in the quasicategorical setting: proving, in analogy with the classical categorical case, that the monadic forgetful functor of the quasicategory of algebras for a homotopy coherent monad creates all limits that exist in the base quasicategory, regardless of whether its functor part preserves those limits. This proof relies upon a more delicate and explicit analysis of the particular weight used to define quasicategories of algebras.
Original language  English 

Pages (fromto)  133 
Number of pages  33 
Journal  Homology, Homotopy and Applications 
Volume  17 
Issue number  1 
DOIs  
Publication status  Published  2015 
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Dive into the research topics of 'Completeness results for quasicategories of algebras, homotopy limits, and related general constructions'. Together they form a unique fingerprint.Projects
 1 Finished

Structural homotopy theory: a categorytheoretic study
Street, R., Lack, S., Verity, D., Garner, R., MQRES, M., MQRES 3 (International), M. 3., MQRES 4 (International), M. & MQRES (International), M.
1/01/13 → 31/12/16
Project: Research