# Fibrations and Yoneda's lemma in an ∞-cosmos

@article{Riehl2017FibrationsAY, title={Fibrations and Yoneda's lemma in an ∞-cosmos}, author={Emily Riehl and Dominic R. Verity}, journal={Journal of Pure and Applied Algebra}, year={2017}, volume={221}, pages={499-564} }

Abstract We use the terms ∞-categories and ∞-functors to mean the objects and morphisms in an ∞-cosmos: a simplicially enriched category satisfying a few axioms, reminiscent of an enriched category of fibrant objects. Quasi-categories, Segal categories, complete Segal spaces, marked simplicial sets, iterated complete Segal spaces, θ n -spaces, and fibered versions of each of these are all ∞-categories in this sense. Previous work in this series shows that the basic category theory of… Expand

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