Geodesic
On the construction of limits and colimits in ∞-categories
Theory and applications of categories, Tome 35 (2020), pp. 1101-1158.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

In previous work, we introduce an axiomatic framework within which to prove theorems about many varieties of infinite-dimensional categories simultaneously. In this paper, we establish criteria implying that an ∞-category --- for instance, a quasi-category, a complete Segal space, or a Segal category --- is complete and cocomplete, admitting 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 reflects limits in a suitable sense, and deduce our main theorems as a consequence.
Publié le :
Classification : 18A30, 18G55, 55U35, 55U40
Keywords: infinity category, limit, colimit 
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     author = {Emily Riehl and Dominic Verity},
     title = {On the construction of limits and colimits in \ensuremath{\infty}-categories},
     journal = {Theory and applications of categories},
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     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a29/}
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Emily Riehl; Dominic Verity. On the construction of limits and colimits in ∞-categories. Theory and applications of categories, Tome 35 (2020), pp. 1101-1158. http://geodesic.mathdoc.fr/item/TAC_2020_35_a29/