Definition 5.36. ([Anel et al. 2024, Section 2.2.7])
Let \(L\) be an acyclic class in \(T\). We define the décalage of \(L\) by
\[D(L) := \{\,u \in L \mid \Delta_u \in L\,\} \subseteq L.\]
We inductively define \(D^n(L)\) by \(D^0(L) := L\) and \(D^{n+1}(L) := D(D^n(L))\). Finally, we set \(D^{\infty}(L) := \cap_n D^n(L)\).
References
- Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal. Left-exact localizations of ∞-topoi. II: Grothendieck topologies. J. Pure Appl. Algebra, 228 (3), 63. 2024.