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.