# Topoi of parametrized objects

## Marc Hoyois

We give necessary and sufficient conditions on a presentable $\infty$-category $C$ so that families of objects of $C$ form an $\infty$-topos. In particular, we prove a conjecture of Joyal that this is the case whenever $C$ is stable.

Keywords: Higher topos theory

2010 MSC: 18B25, 55P99

Theory and Applications of Categories, Vol. 34, 2019, No. 9, pp 243-248.

Published 2019-03-18.

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