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Abstract
In previous work, we introduce an axiomatic framework within which to prove theorems about many varieties of inﬁnitedimensional categories simultaneouslyIn this paper, we establish criteria implying that an ∞category — for instance, a quasicategory, a complete Segal space, or a Segal category — is complete and cocompleteadmitting limits and colimits indexed by any small simplicial set. Our strategy is to build (co)limits of diagrams indexed by a simplicial set inductively from (co)limits of restricted diagrams indexed by the pieces of its skeletal ﬁltration. We show directly that the modules that express the universal properties of (co)limits of diagrams of these shapes are reconstructible as limits of the modules that express the universal properties of (co)limits of the restricted diagrams. We also prove that the Yoneda embedding preserves and reﬁects limits in a suitable sense, and deduce our main theorems as a consequence.
Original language  English 

Pages (fromto)  11011158 
Number of pages  58 
Journal  Theory and Applications of Categories 
Volume  35 
Issue number  30 
Publication status  Published  2020 
Keywords
 infinity category
 limit
 colimits
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Dive into the research topics of 'On the construction of limits and colimits in ∞categories'. Together they form a unique fingerprint.Projects
 2 Finished

Working synthetically in higher categorical structures
Lack, S., Verity, D., Garner, R. & Street, R.
19/06/19 → 18/06/22
Project: Other

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