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Abstract
In this paper we redevelop the foundations of the category theory of quasicategories (also called ∞categories) using 2category theory. We show that Joyal's strict 2category of quasicategories admits certain weak 2limits, among them weak comma objects. We use these comma quasicategories to encode universal properties relevant to limits, colimits, and adjunctions and prove the expected theorems relating these notions. These universal properties have an alternate form as absolute lifting diagrams in the 2category, which we show are determined pointwise by the existence of certain initial or terminal vertices, allowing for the easy production of examples.All the quasicategorical notions introduced here are equivalent to the established ones but our proofs are independent and more "formal". In particular, these results generalise immediately to model categories enriched over quasicategories.
Original language  English 

Pages (fromto)  549642 
Number of pages  94 
Journal  Advances in Mathematics 
Volume  280 
DOIs  
Publication status  Published  6 Aug 2015 
Keywords
 Quasicategories
 2Category theory
 Formal category theory
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Projects
 1 Finished

Applicable categorical structures
Street, R., Johnson, M., Lack, S., Verity, D. & Lan, R.
1/01/10 → 30/06/14
Project: Research