# 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}
}
• Published 2017
• Mathematics
• Journal of Pure and Applied Algebra
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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