Remark 3.38.
The term “hypercomplete” is historical but slightly misleading: hypercompleteness is a separation condition rather than a completeness condition. “Postnikov separated” might have been a better term. In [Anel et al. 2025], the authors use the term “hyperreduced” instead.
References
- Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal. Left-exact localizations of $\infty$-topoi III: The acyclic product. 2025.