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Abstract
In this paper we prove that various quasicategories whose objects are ∞categories in a very general sense are complete: admitting limits indexed by all simplicial sets. This result and others of a similar flavor follow from a general theorem in which we characterize the data that is required to define a limit cone in a quasicategory constructed as a homotopy coherent nerve. Since all quasicategories arise this way up to equivalence, this analysis covers the general case. Namely, we show that quasicategorical limit cones may be modeled at the pointset level by pseudo homotopy limit cones, whose shape is governed by the weight for pseudo limits over a homotopy coherent diagram but with the defining universal property up to equivalence, rather than isomorphism, of mapping spaces. Our applications follow from the fact that the (∞, 1) categorical core of an ∞cosmos admits weighted homotopy limits for all flexible weights, which includes in particular the weight for pseudo cones.
Original language  English 

Pages (fromto)  669716 
Number of pages  48 
Journal  Applied Categorical Structures 
Volume  28 
Issue number  4 
DOIs  
Publication status  Published  Aug 2020 
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Projects
 1 Finished

Monoidal categories and beyond: new contexts and new applications
Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.
30/06/16 → 17/06/19
Project: Research